Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem
In this article we analyze a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $\epsilon$. We show that the problem has solutions for $\epsilon$ small enough and we investigate the dependence of a s...
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| Format: | Article |
| Language: | English |
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Texas State University
2019-04-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/53/abstr.html |
| Summary: | In this article we analyze a boundary value problem for the Laplace equation
with a nonlinear non-autonomous transmission conditions on the boundary of
a small inclusion of size $\epsilon$. We show that the problem has solutions
for $\epsilon$ small enough and we investigate the dependence of a specific
family of solutions upon $\epsilon$. By adopting a functional analytic
approach we prove that the map which takes $\epsilon$ to
(suitable restrictions of) the corresponding solution can be represented
in terms of real analytic functions. |
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| ISSN: | 1072-6691 |