Grupo Dinámica No Lineal
Departamento de Matemática Aplicada
Universidad Pontificia Comillas
Alberto Aguilera 25, 28015-Madrid, Spain
email: scano@comillas.edu
Santiago Cano-Casanova
Abstract:
This article concerns the positive solutions of a boundary-value problem
constituted by a linear elliptic partial differential equation, subject to
nonlinear mixed boundary conditions containing spatial heterogeneities with
arbitrary sign along the boundary. The results obtained in this work provide
us the global bifurcation diagram of positive solutions, the pointing behavior
of them when the parameters change and the dynamics of the positive solutions
of the associated parabolic problem. The main contribution of this paper is to
give general results about existence, uniqueness, stability and pointing
behavior of positive solutions, for boundary-value problems with nonlinear
boundary conditions of mixed type containing spatial heterogeneities.
The main technical tools used to develop the mathematical analysis are local
and global bifurcation, monotonicity techniques, the Characterization of the
Strong Maximum Principle given by Amann and Lopez-Gomez [5]
blow up arguments and some of the techniques used in the previous works
[19,20,33,34]. The results obtained in this paper are the natural
continuation of the previous ones in [11].
Submitted January 12, 2018. Published September 12, 2018.
Math Subject Classifications: 35J65, 35J25,35B09, 35B35, 35B40.
Key Words: Nonlinear mixed boundary conditions; positive solutions;
spatial heterogeneities; nonlinear flux with arbitrary sign;
blow up in finite time; elliptic and parabolic boundary value problems.
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Santiago Cano-Casanova Grupo Dinámica No Lineal Departamento de Matemática Aplicada Universidad Pontificia Comillas Alberto Aguilera 25, 28015-Madrid, Spain email: scano@comillas.edu |
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