The blow-up problem for a semilinear parabolic equation with a potential
link https://doi.org/10.1016/j.jmaa.2007.01.079get_app2024-04-17. The blow-up problem for a semilinear parabolic equation with a potential.pdf
account_box Cortazar, Carmenaccount_box Elgueta, Manuelaccount_box Rossi, Julio D.
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Let Omega be a bounded smooth domain in R-N. We consider the problem u(t) = Delta u + V(x)u(P) in Omega x [0, T), with Dirichlet boundary conditions u = 0 on partial derivative Omega x [0, T) and initial datum u (x, 0) = M phi (x) where M >= 0, phi is positive and compatible with the boundary condition. We give estimates for the blow-up time of solutions for large values of M. As a consequence of these estimates we find that, for M large, the blow-up set concentrates near the points where phi(P-1) V attains its maximum. (c) 2007 Elsevier Inc. All rights reserved.
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| Autor | Cortazar, Carmen Elgueta, Manuel Rossi, Julio D. |
| Título | The blow-up problem for a semilinear parabolic equation with a potential |
| Revista | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
| ISSN | 0022-247X |
| Volumen | 335 |
| Número de publicación | 1 |
| Página inicio | 418 |
| Página final | 427 |
| Fecha de publicación | 2007 |
| Resumen | Let Omega be a bounded smooth domain in R-N. We consider the problem u(t) = Delta u + V(x)u(P) in Omega x [0, T), with Dirichlet boundary conditions u = 0 on partial derivative Omega x [0, T) and initial datum u (x, 0) = M phi (x) where M >= 0, phi is positive and compatible with the boundary condition. We give estimates for the blow-up time of solutions for large values of M. As a consequence of these estimates we find that, for M large, the blow-up set concentrates near the points where phi(P-1) V attains its maximum. (c) 2007 Elsevier Inc. All rights reserved. |
| Derechos | acceso restringido |
| DOI | 10.1016/j.jmaa.2007.01.079 |
| Editorial | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Enlace | |
| Id de publicación en WoS | WOS:000248445800032 |
| Paginación | 10 páginas |
| Palabra clave | blow-up semilinear parabolic equations HEAT-EQUATIONS DIFFUSION |
| Tipo de documento | artículo |