Singular Perturbations Method for Partial Di¤erential Equations
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Date
2021
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Publisher
Université de M'sila
Abstract
In this thesis we deal with anisotropic singular perturbations of some integro-differential problems,
depending on a small parameter of perturbation # > 0. These problems involve elliptic
equations of semilinear and quasilinear types with some non-local nonlinearities. Using a
variational approach, we establish the existence of their solutions as critical points of some
C1-functionals in anisotropic weighted Sobolev type spaces. The main goal of this thesis is to
study the asymptotic behaviour of these solutions with respect to the parameter of perturbation #.
As # ! 0, some existence results for non-standard integro-differential problems are established.
Keywords and phrases:
Anisotropic singular perturbations, asymptotic behaviour, elliptic problems, non-local terms,
critical points, semilinear problems, quasilinear problems.