Artículo

Ferreira, R.; De Pablo, A.; Pérez-LLanos, M.; Rossi, J.D. "Critical exponents for a semilinear parabolic equation with variable reaction" (2012) Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 142 A(5):1027-1042
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Abstract:

We study the blow-up phenomenon for non-negative solutions to the following parabolic problem: [equation presented] where 0 < p = min p p(x) max p = p+ is a smooth bounded function. After discussing existence and uniqueness, we characterize the critical exponents for this problem. We prove that there are solutions with blow-up in finite time if and only if p+ > 1. When ω = ℝ N we show that if p > 1 + 2/N, then there are global non-trivial solutions, while if 1 < p p+ 1 + 2/N, then all solutions to the problem blow up in finite time. Moreover, in the case when p < 1 + 2/N < p+, there are functions p(x) such that all solutions blow up in finite time and functions p(x) such that the problem possesses global non-trivial solutions. When ω is a bounded domain we prove that there are functions p(x) and domains ω such that all solutions to the problem blow up in finite time. On the other hand, if ω is small enough, then the problem possesses global non-trivial solutions regardless of the size of p(x). © 2012 Royal Society of Edinburgh.

Registro:

Documento: Artículo
Título:Critical exponents for a semilinear parabolic equation with variable reaction
Autor:Ferreira, R.; De Pablo, A.; Pérez-LLanos, M.; Rossi, J.D.
Filiación:Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, 1428 Buenos Aires, Argentina
Departamento de Análisis Matemático, Universidad de Alicante, Apartado de correos 99, 03080 Alicante, Spain
Año:2012
Volumen:142 A
Número:5
Página de inicio:1027
Página de fin:1042
DOI: http://dx.doi.org/10.1017/S0308210510000399
Título revista:Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Título revista abreviado:Proc. R. Soc. Edinburgh Sect. A Math.
ISSN:03082105
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03082105_v142A_n5_p1027_Ferreira

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Citas:

---------- APA ----------
Ferreira, R., De Pablo, A., Pérez-LLanos, M. & Rossi, J.D. (2012) . Critical exponents for a semilinear parabolic equation with variable reaction. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 142 A(5), 1027-1042.
http://dx.doi.org/10.1017/S0308210510000399
---------- CHICAGO ----------
Ferreira, R., De Pablo, A., Pérez-LLanos, M., Rossi, J.D. "Critical exponents for a semilinear parabolic equation with variable reaction" . Proceedings of the Royal Society of Edinburgh Section A: Mathematics 142 A, no. 5 (2012) : 1027-1042.
http://dx.doi.org/10.1017/S0308210510000399
---------- MLA ----------
Ferreira, R., De Pablo, A., Pérez-LLanos, M., Rossi, J.D. "Critical exponents for a semilinear parabolic equation with variable reaction" . Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 142 A, no. 5, 2012, pp. 1027-1042.
http://dx.doi.org/10.1017/S0308210510000399
---------- VANCOUVER ----------
Ferreira, R., De Pablo, A., Pérez-LLanos, M., Rossi, J.D. Critical exponents for a semilinear parabolic equation with variable reaction. Proc. R. Soc. Edinburgh Sect. A Math. 2012;142 A(5):1027-1042.
http://dx.doi.org/10.1017/S0308210510000399