Publications before 2010

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_TOC_ === Year 2002 === # J. M. Arrieta, N. Consul, A. Rodríguez-Bernal “Pattern Formation from boundary reaction”''' '''''Fields Inst. Commun.'', 31, pp. 13-18, Amer. Math. Soc., Providence, RI, (2002).''' '''<br/> # X. Biao Lin, I. Bosch “Heteroclinic and periodic cycles in a perturbed convection model”'' Journal of Differential Equations'' 182 pp. 219-265 (2002)<br/> # R. Ferreira, P. Groisman y J. D. Rossi, “Numerical Blow-up for a nonlinear problem with a nonlinear boundary condition”'' Math. Models and Methods in Applied Sciences'', 12, 461--483, 2002<br/> # R. Ferreira, V. A. Galaktionov y J. L. Vázquez, “Uniqueness of Asymptotic Profiles for and extinction Problem”'' Nonlinear Analysis T. M. A.'', 50, 495--507, 2002<br/> # R. Ferreira, F. Quiros y J. D. Rossi “The balance between nonlinear inwards and outwards boundary-flux for nonlinear heat equations” ''Journal of Differential Equation'', 184, 259--282, 2002<br/> # A. Jiménez-Casas and A. Rodríguez-Bernal. Asymptotic behaviour for a phase field model in higher order Sobolev spaces. ''Rev. Mat. Complut.'', 15(1):213-248, 2002.<br/> # A. Rodríguez-Bernal. Some qualitative dynamics of nonlinear boundary conditions. ''Internat. J. Bifur. Chaos Appl. Sci. Engrg.'', 12(11):2333-2342. Spatio-temporal comp lexity. (2002)<br/> # A. Rodríguez-Bernal. Attractors for parabolic equations with nonlinear boundary conditions, critical exponents, and singular initial data. ''J. Differential Equations,'' 181(1):165-196, 2002.<br/> # R. Dager, E. Zuazua “Spectral boundary controllability of networks of strings”, C.R. Acad. Sci. Paris, Serie I, 334 (7), 545-550, (2002)<br/> === Year 2003 === # J. Fernández Bonder, R. Ferreira y J. D. Rossi, “Uniform bounds for the best Sobolev trace constant” ''Advanced Nonlinear Studies'', 3, 181--192, 2003<br/> # R. Ferreira, A. de Pablo, F. Quiros y J. D. Rossi, “The blow-up profile for a fast diffusion equation with a nonlinear boundary condition” ''Rocky Mountain J. Math,'' 33, 123--146, 2003<br/> # R. Ferreira y J. L. Vázquez “Study of self-similarity for the fast difusión equation” ''Advances in Differential Equations'', 8, 1125--1152, 2003<br/> # R. Ferreira, P. Groisman y J. D. Rossi , “An adaptive numerical scheme for a parabolic problem with blow-up”'' IMA Journal of Numerical Análisis'', 23, 439--463, 2003<br/> # M. Negreanu, E. Zuazua, “Uniform boundary controllabillity of a discrete 1-D wave equation” , ''System and Control Letters'', 48, Issues 3-4 pp 261-279 (2003)<br/> # M. Negreanu, E. Zuazua, “A 2-d grid algorithm for the 1-d wave equation” Proceedings of the Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Waves 2003, Physcis and Astronomy, pp. 213-217, Springer (2003)<br/> # R. Rodríguez del Río, E. Zuazua, “Series de Fourier y fenómeno de Gibbs”, Cubo Matemática Eduacional, 5 pp. 185-224 (2003)<br/> === Year 2004 === # J.M. Arrieta "El Cálculo y la Modelización Matemática", en R. Rodríguez, E. Zuazua, ''De la Aritmética al Análisis: Historia y Desarrollo reciente en Matemáticas,'' Aulas de Verano, Instituto Superior de Formación del Profesorado, Ministerio de Educación y Ciencia,pp 11-57 (2004)<br/> # J. M. Arrieta, A.N. Carvalho "Spectral Convergence and Nonlinear Dynamics for Reaction-Diffusion Equations under Perturbations of the Domain" ''Journal of Diff. Equations ''199, pp. 143-178 (2004)<br/> # J. M. Arrieta, J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal, "Asymptotic Behavior and Attractors for Reaction Diffusion Equations in Unbounded Domains" ''Nonlinear Analysis, ''56, pp. 515-554 (2004) <br/> # J. M. Arrieta, N. Consul, A. Rodríguez-Bernal, "Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary" ''Z.. Angew. Math. Phys. ''55, pp. 1-14 (2004) <br/> # J. M. Arrieta, J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal, "Linear parabolic equations in locally uniform spaces" ''Mathematical Models and Methods in Applied Sciences'', 14, n. 2, 253-294 (2004)<br/> # J. M. Arrieta, A. Rodríguez-Bernal and P. Souplet, "Boundedness of Global Solutions for Nonlinear Parabolic Equations involving Gradient Blow-up Phenomena" ''Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. ''Issue 1, Volume 3/2004, Series 5, pp 1-15, (2004) <br/> # J. M. Arrieta, A. Rodríguez-Bernal "Localization on the boundary of blow-up for reaction-diffusion equations with nonlinear boundary conditions" ''Communications in Partial Differential Equations'' 29, 7&8, pp. 1127-1148 (2004) <br/> # J.M. Arrieta, A. Rodríguez-Bernal "Non well posedness of parabolic equations with supercritical nonlinearities" ''Communications in Contemporary Mathematics'' 6, n 5, pp. 733-764 (2004)<br/> # E. Chasseigne y R.Ferreira, “Monotone approximations of Green functions” ''Comptes Rendus Mathématique.'' Académie des Sciences. Paris, 339, 395--400, 2004<br/> # R. Ferreira, P. Groisman y J. D. Rossi., “Numerical blow-up for the porous medium equation with a source”'' Numerical Methods for Partial Differential Eq,'' 20, 552--575, 2004<br/> # R. Ferreira, A. de Pablo, F. Quiros y J. D. Rossi, “Superfast quenching”'' Journal Differential Equations'', 199, 189--209, 2004<br/> # M. Negreanu, E. Zuazua “Discrete Ingham inequalities and applications”, ''CRAS Paris'', Serie I. Math 338 pp 281-286 (2004)<br/> # L. Popescu and A. Rodríguez-Bernal. On a singularly perturbed wave equation with dynamic boundary conditions. ''Proc. Roy. Soc. Edinburgh ''Sect. A, 134(2):389-413, 2004.<br/> # R. Dager, “Networks of strings: modelization and control of vibrations”, e-STA, vol 1, (2004)<br/> # R. Dager, “Observation and control of vibrations in tree-shaped networks of strings” SIAM Journal on Control and Optimization 43, 590-623, (2004)<br/> ===Year 2005 === # J.M. Arrieta, A. Rodríguez-Bernal. "Ill posed problems with supercritical nonlinearities''. International Conference on Differential Equations (EQUADIFF'03) Hasselt, Belgium. World Scientific, pp 277 280, (2005) , <br/> # J.M. Arrieta, A. Jiménez-Casas, A. Rodríguez-Bernal "Nonhomogenous flux condition as limit of localized reactions''. International Conference on Differential Equations (EQUADIFF'03) Hasselt, Belgium. World Scientific, pp 293-295, (2005), <br/> # J.M. Arrieta, S. M. Bruschi "Problemas de valor de fronteira em domínios com oscilaçōes na fronteira", ''Seminario Brasileiro de Análise,'' Edición nº 62, Noviembre (2005), <br/> # R. Ferreira, A. de Pablo, F. Quiros y J. L. Vázquez, “Blow-up. El problema matemático de explosión para ecuaciones y sistemas de reacción difusión” ''Boletín de la Soc. Española de Matemática Aplicada'', 32, 75-111, 2005<br/> # P. Quittner and A. Rodríguez-Bernal. Complete and energy blow-up in parabolic problems with nonlinear boundary conditions. ''Nonlinear Anal. TMA'', 62(5):863-875, (2005).<br/> # A. Rodríguez-Bernal and A. Vidal-López. Extremal equilibria and asymptotic behavior of parabolic nonlinear reaction-diffusion equations. In ''Nonlinear elliptic and parabolic problems: A Special Tribute to the Work of H. Amann.'', volume 64 of Progr. Nonlinear Differential Equations Appl., pages 509-516. Birkhäuser, Basel, (2005).<br/> # A. Rodríguez-Bernal. Parabolic equations in locally uniform spaces. In ''Nonlinear elliptic and parabolic problems,'' volume 64 of Progr. Nonlinear Differential Equations Appl., pages 421-432. Birkhäuser, Basel, (2005).<br/> # A. Rodríguez-Bernal and R. Willie. Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem. ''Discrete Contin. Dyn. Syst.'' Ser. B, 5(2):385-410, (2005).<br/> # R. Ferreira, A. de Pablo y M. Pérez-Llanos, “Numerical blow-up for the p-laplacian equation with a source”, ''Computational Methods in Applied Mathematics ''5, 137-154, (2005)<br/> # R. Ferreira, A. de Pablo, F. Quiros y J. D. Rossi, “On the quenching set for a fast diffusion equation.Regional quenching”'', Proceedings of the Royal Society of Edinburgh. Section A, ''135, 585—601, (2005)<br/> # A. Jiménez-Casas, “Metastable solutions for the thin-interface limit of a phase-field model” ''Nonlinear Analysis'', ''Volume ''63, Issues 5-7, 963-970, (2005)<br/> # A. Jiménez-Casas, “Well posedness and asymptotic behavior of a closed loop thermosyphon”, World Scientific Publications pp: 59-74, (2005)<br/> ===Year 2006 === # R. Dager, E. Zuazua, “Wave propagation, observation and control of 1-D flexible multi-structures”, Mathematiques et Applications 50, Springer-Berlag Berlin (2006), <nowiki>x+221 pp. ISBN: 978-3-540-27239-9; 3-540-27239-9 [LIBRO DE INVESTIGACIÓN]</nowiki> # I. Bosch, A. M. Minzoni, “Chaotic behavior in a singularly perturbed system” ''Nonlinearity'' 19, 1535-1551 (2006)<br/> # M. Negreanu, E. Zuazua “Discrete Ingham inequalities and applications”, ''SIAM Journal of Numerical Analysis,'' Volume 44, Issue I (2006) pp 412-4448<br/> # A. Rodríguez-Bernal and A. Vidal, “Asymptotic behavior of positive solutions of nonautonomous reaction-diffusion equations”, ''Bol. Soc. Esp. Mat. Apl.'' 34, 99-104 (2006) <br/> # J. C. Robinson, A. Vidal López, “Minimal periods of semilinear evolution equations with Lipschitz nonlinearity”. ''Jounal of Differential Equations'', Vol. 220 (2), 396-406 (2006).<br/> # J.M. Arrieta, S. M. Bruschi "Boundary Oscillations and Nonlinear Boundary Conditions", ''Comptes Rendus Mathematique, ''t. 343, Series I, pp. 99-104 (2006)<br/> # J.M. Arrieta, A. Rodríguez-Bernal, J. Valero "Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity", ''International Journal of Bifurcation and Chaos'' 16, n. 10, pp. 2965-2984 (2006)<br/> # J.M. Arrieta A.N. Carvalho and G. Lozada-Cruz "Dynamics in dumbbell domains I. Continuity of the set of equilibria" ''Journal of Differential Equations ''231, Issue 2, pp. 551-597, (2006),<br/> # R. Ferreira, A. de Pablo y J. L. Vázquez, “Classification of blow-up with nonlinear diffusion and localized reaction”, ''Journal Differential Equations ''231, 195—211, (2006)<br/> # R. Ferreira, A. de Pablo, G. Reyes y A. Sánchez, “The interfaces of an inhomogeneous porous médium equation with convection”'' Communications in Partial Differential Equation''s , 31, 497—514, (2006)<br/> # R. Ferreira, A. de Pablo y J. D. Rossi, “Blow-up for a degenerate diffusion problem not in divergence form”, ''Indiana University Mathematics Journal '', 55, 955—974, (2006)<br/> # R. Ferreira, A. de Pablo, F. Quiros y J. D. Rossi, “Non-simultaneous quenching in a system of heat equations coupled at the boundary”'' Zeitschrift fur Angewandte Mathematik und Physik '', 57, 586—594, (2006).<br/> # R. Pardo, V. M. Pérez-García, “Dissipative solutions that cannot be trapped”, ''Phys. Rev. Lett.'' 97, (2006). <br/> # R. Dager, A. Presa, “Duality of the space of germs of harmonic vector fields on a compact”, C.R. Acad. Sci. Paris, Serie I, 343 (1), 19-22, (2006)<br/> # R. Dager, “Insensitizing controls for the 1-D wave equation”, SIAM Journal on Control and Optimization 45, 1758-1768, (2006)<br/> ===Year 2007 === # J.M. Arrieta, R. Pardo, A. Rodríguez-Bernal "Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity", ''Proc. of the Royal Society of Edinburgh A,'' Vol.137, Issue 02, 225-252. (2007),<br/> # A. Rodríguez-Bernal, R. Willie, “Nesting inertial manifolds of reaction-diffusion equations and large diffusivity. ''Nonlinear Analisis'' 67, 70-93 (2007)<br/> # A. Rodríguez-Bernal, A. Vidal, “Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems”, ''Disc. Cont. Dyn. Systems ''18, 537--567, (2007)<br/> # J.A. Langa, J.C. Robinson, A.Rodríguez-Bernal, A. Suárez, A. Vidal, “Existence and non-existence of unbounded forward attractor for a class of nonautonomous reaction diffusion equations”. ''Disc. Cont. Dyn. Systems ''18, 483—497, (2007)<br/> # J.M. Arrieta, S.M. Bruschi “Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation”, ''Mathematical Models and Methods in Applied Sciences'' 17, nº 10 (2007)<br/> # R. Ferreira, A. de Pablo y J. D. Rossi, “Blow-up with logarithmic nonlinearities”, ''Journal Differential Equations ''240, Issue 1, Pages 196-215 (2007)<br/> # J.C. Robinson, A. Rodríguez-Bernal, A. Vidal-López, “Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems”, Journal of Differential Equations 238, 289-337 (2007)<br/> # U. Brauer, L. Karp, “Local existence of classical solutions of the Einstein-Euler system using weighted Sobolev spaces of fractional order”, Comptes Rendus Mathematique 345, pp 49-54 (2007)<br/> # J. A. Langa, J. C. Robinson, A. Suárez, A. Vidal-López, “The stability of attractors for non-autonomous perturbation of gradient-like systems”, ''Journal of Differential Equations'' 234, 605-627 (2007). <br/> # J. M. Arrieta and A. Rodríguez-Bernal, “Blow up versus global boundedness of solutions of reaction diffusion equations with nonlinear boundary conditions”, Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 1-7 <br/> # J. M. Arrieta, A. Jimenéz-Casas and A. Rodríguez-Bernal, “Robin type conditions arising from concentrated potentials”, Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 157-164 <br/> # A. de Pablo, M. Pérez-Llanos and R. Ferreira''', “'''Numerical blow-up for the ''p''-Laplacian equation with a nonlinear source” Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 363-367<br/> # J. M. Arrieta, N. Moya, A. Rodríguez-Bernal''', “'''Dissipative dynamics of reaction diffusion equations in ''R^N” ''Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007), pp 405-414.<br/> # A. Rodríguez-Bernal and A. Vidal-López''', “'''Extremal equilibria for parabolic non-linear reaction-diffusion equations”, Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 531-539 <br/> # J.M. Arrieta, J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal, "Dissipative parabolic equations in locally uniform spaces", ''Mathematische Nachrichten ''280, Issue 15 (2007)<br/> #Bogoya, Mauricio; Ferreira, Raul; Rossi, Julio D. Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models. Proc. Amer. Math. Soc. 135 (2007), no. 12, 3837--3846 ===Year 2008 === #J.M. Arrieta:" On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions" Proceedings of the American Mathematical Society 136, Issue 1, pp. 151-160 (2008) #J.M. Arrieta, N. Moya, A. Rodríguez-Bernal: "On the finite dimension of attractors of parabolic problems in <math>R^N </math> with general potentials", Nonlinear Analysis, Theory Methods and Applications 68, Issue 5, pp. 1082-1099 (2008) #J.M. Arrieta, A. Jimenez-Casas, A. Rodriguez-Bernal "Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating in the boundary" Revista Matemática Iberoamericana, 24 nº 1, pp. 183- 211 (2008) # A. Jiménez Casas, "Invariant regions and global existence for a phase field model", Discrete and Cont. Dynam. Systems. 1, nº 2 273-281 (2008) <br/> # M. Bogoya, R. Ferreira, J.D. Rossi, "A nonlocal nonlinear diffusion equation with blowing up boundary conditions", Journal of Mathematical Analysis and Applications 337, nº 2, 1284-1294 (2008) <br/> # A. Rodríguez-Bernal, A. Vidal-López, "Semiestable extremal ground states for nonlinear evolution equations in unbounded domains", Journal of Mathematical Analysis and Applications 338, nº 1, 675-694 (2008)<br/> # J.M. Arrieta, A. Rodríguez-Bernal, J. Rossi, "The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary", Proceedings of the Royal Society of Edinburgh 138A 223-237 (2008),<br/> # Ferreira, Raúl; de Pablo, Arturo; Pérez-Llanos, Mayte; Rossi, Julio D. Incomplete quenching in a system of heat equations coupled at the boundary. J. Math. Anal. Appl. 346 (2008), no. 1, 145--154. # A. Rodríguez-Bernal, A. Vidal-López, Extremal equilibria for nonlinear parabolic equations in bounded domains and applications”. Journal of Di?erential Equations 244, 2983-3030 (2008). <br/> ===Year 2009 === #R. Ferreira, “Numerical quenching for the semilinear heat equation with a singular absorption”, J. Comput. Appl. Math. 228, 92—103, (2009) #J.M. Arrieta, R. Pardo, A. Rodríguez-Bernal, "Equilibria and global dynamics of a problem with bifurcation from infinity", Journal of Differential Equations 246, pp. 2055-2080 (2009). #R. Pardo, V.M. Pérez-García, ``Localization phenomena in Nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates. Physica D: Nonlinear Phenomena, Vol. 238, 1352-1360. (2009) #J.M. Arrieta, A. N. Carvalho, G. Lozada-Cruz , “Dynamics in dumbbell domains II. The limiting problem” Journal of Differential Equations 247, pp 174-202 (2009) #J.M. Arrieta, A. N. Carvalho, G. Lozada-Cruz , “Dynamics in dumbbell domains III. Continuity of attractors”, Journal of Differential Equations, 247, pp. 225-259, (2009) #J. Langa, J. Robinson, A. Rodriguez-Bernal, A. Suárez, “Permanence and asymptotically stable complete trajectories for non-autonomous Lotka-Volterra models with diffusion”, SIAM J. Math. Anal., Volume 40, Pages 2179-2216, (2009) #A. Rodríguez-Bernal, “Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations”, Discrete and Continuous Dynamical Systems A., vol. 25, 1003-1032 (2009). #A. Jiménez Casas, A. Rodríguez Bernal, “Asymptotic behaviour of a parabolic problem with terms concentrated in the boundary”, Nonlinear Analysis, Theory Methods and Applications 71, pp: e-2377-2383 (2009) #A.Jiménez-Casas, A. Rodríguez–Bernal, “Atractor de un problema parabólico con términos concentrados en la frontera”. Actas CEDYA 2009. XXI CEDYA / XI CMA. Ciudad Real. Sema. 2009. ISBN: 978-84-692-64 #J.Cholewa, A. Rodríguez Bernal,“Algunas propiedades dinámicas de semigrupos monótonos y aplicaciones”. Actas CEDYA 2009. XXI CEDYA / XI CMA. Ciudad Real. Sema. 2009. ISBN: 978-84-692-64 #Rodríguez Bernal, A.Vidal López, “Dinámica asintótica de problemas de reacción-difusión con balance no lineal entre la reacción en el interior y en la frontera” Actas CEDYA 2009. XXI CEDYA / XI CMA. Ciudad Real. Sema. 2009. (6 páginas). ISBN: 978-84-692-64 #R. Pardo, H. Herrero, “Existencia de soluciones para un problema de Bénard-Marangoni”. Actas CEDYA 2009. XXI CEDYA / XI CMA. Ciudad Real. Sema. 2009. (6 páginas). ISBN: 978-84-692-64 #R. Ferreira, M. Pérez-Llanos, Numerical quenching of a system of equations coupled at the boundary, Mathematical Methods in the Applied Sciences, 32, pp. 2439-2459, (2009) === Year 2010 === #J. M. Arrieta, R. Ferreira, A. de Pablo y J. D. Rossi, Stability of the blow-up time and the blow-up set under perturbations, Discrete and Continuous Dynamical Systems A 26, # 1, pp 43-61 (2010) #J.M. Arrieta, N. Consul and S. Oliva , “Cascades of Hopf bifurcations from boundary delay”, Journal of Mathematical Analysis and Applications 361, pp. 19-37 (2010) #J. M. Arrieta, D. Krejcirik, "Geometric vs. spectral convergence for the Neumann Laplacian under exterior perturbations of the domain", Integral methods in science and engineering. Vol. 1, pp:9-19, Birkhäuser Boston, Inc., Boston, MA, (2010) #J. M. Arrieta, S.M. Bruschi, "Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of non uniform Lispschitz deformation" Discrete and Continuous Dynamical Systems B, Volume 14, Number 2, pp. 327-351 (2010) #J. M. Arrieta, M.C. Pereira, “Elliptic problems in thin domains with highly oscillating boundaries”, Bolletin de la Sociedad Española de Matemática Aplicada 51, pp:17-24 (2010) #J.M. Arrieta, N. Consul, S. Oliva “On the supercriticality of the first Hopf bifurcation in a delay boundary problem” International Journal of Bifurcation and Chaos 20, #9 (2010) #J.M. Arrieta, R. Pardo, A. Rodríguez-Bernal, “Infinite resonant solutions and turning points in a problem with unbounded bifurcation” International Journal of Bifurcation and Chaos 20, #9 (2010) #J.A. Langa, A. Rodríguez-Bernal and A. Suárez, "The sub-supertrajectory method. Application to the nonautonomous competition Lotka-Volterra model". Bol. Soc. Esp. Mat. Apl. 51, 91--98 (2010). #J.A. Langa, A. Rodríguez-Bernal and A. Suárez, "On the long time behaviour of non-autonomous Lotka-Volterra models with diffusion via the sub-super trajectory method". Journal of Differential Equations 249, 414--445 (2010). #J. Cholewa, A. Rodríguez-Bernal, "Extremal equilibria for monotone semigroups with applications to evolutionary equations". Journal of Differential Equations 249, 485--525 (2010).

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