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Abstract:

This work is devoted to the analysis of the asymptotic behavior of positive solutions to some problems of variable exponent reaction-diffusion equations, when the boundary condition goes to infinity (large solutions). Specifically, we deal with the equations Δu = up(x), Δu = -m(x)u + a(x)up(x) where a(x) ≥ a0 > 0, p(x) ≥ 1 in Ω, and Δu = ep(x) where p(x) ≥ 0 in Ω. In the first two cases p is allowed to take the value 1 in a whole subdomain Ωc ⊂ Ω, while in the last case p can vanish in a whole subdomain Ωc ⊂ Ω. Special emphasis is put in the layer behavior of solutions on the interphase Γi: = ∂Ωc∩Ω. A similar study of the development of singularities in the solutions of several logistic equations is also performed. For example, we consider -Δu = λ m(x)u-a(x) up(x) in Ω, u = 0 on ∂Ω, being a(x) and p(x) as in the first problem. Positive solutions are shown to exist only when the parameter λ lies in certain intervals: bifurcation from zero and from infinity arises when λ approaches the boundary of those intervals. Such bifurcations together with the associated limit profiles are analyzed in detail. For the study of the layer behavior of solutions the introduction of a suitable variant of the well-known maximum principle is crucial. © 2010 Springer-Verlag.

Registro:

Documento: Artículo
Título:An application of the maximum principle to describe the layer behavior of large solutions and related problems
Autor:García-Melián, J.; Rossi, J.D.; Sabina de Lis, J.C.
Filiación:Departamento de Análisis Matemático, Universidad de La Laguna, C/ Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain
Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atómica, Molecular y Fotónica, Universidad de La Laguna, C/ Astrofísico Francisco, Sánchez s/n, 38203 La Laguna, Spain
Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Año:2011
Volumen:134
Número:1
Página de inicio:183
Página de fin:214
DOI: http://dx.doi.org/10.1007/s00229-010-0391-z
Título revista:Manuscripta Mathematica
Título revista abreviado:Manuscr. Math.
ISSN:00252611
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00252611_v134_n1_p183_GarciaMelian

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Citas:

---------- APA ----------
García-Melián, J., Rossi, J.D. & Sabina de Lis, J.C. (2011) . An application of the maximum principle to describe the layer behavior of large solutions and related problems. Manuscripta Mathematica, 134(1), 183-214.
http://dx.doi.org/10.1007/s00229-010-0391-z
---------- CHICAGO ----------
García-Melián, J., Rossi, J.D., Sabina de Lis, J.C. "An application of the maximum principle to describe the layer behavior of large solutions and related problems" . Manuscripta Mathematica 134, no. 1 (2011) : 183-214.
http://dx.doi.org/10.1007/s00229-010-0391-z
---------- MLA ----------
García-Melián, J., Rossi, J.D., Sabina de Lis, J.C. "An application of the maximum principle to describe the layer behavior of large solutions and related problems" . Manuscripta Mathematica, vol. 134, no. 1, 2011, pp. 183-214.
http://dx.doi.org/10.1007/s00229-010-0391-z
---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D., Sabina de Lis, J.C. An application of the maximum principle to describe the layer behavior of large solutions and related problems. Manuscr. Math. 2011;134(1):183-214.
http://dx.doi.org/10.1007/s00229-010-0391-z