On the mixed boundary value problem for semilinear elliptic equations
| Autor: | Marin Mišur |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
General Computer Science Applied Mathematics Fixed-point theorem Boundary (topology) Domain decomposition methods 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Dirichlet distribution Theoretical Computer Science Elliptic curve symbols.namesake Fixed-point iteration Modeling and Simulation 0202 electrical engineering electronic engineering information engineering symbols Order (group theory) Applied mathematics 020201 artificial intelligence & image processing Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Mathematics and Computers in Simulation. 179:162-177 |
| ISSN: | 0378-4754 |
| Popis: | We investigate the existence of weak solutions of a mixed boundary value problem for second order semilinear elliptic equation. The result is obtained by using regularity estimates for mixed linear elliptic problems and an appropriate fixed point theorem. For the homogeneous problem, we also get a result on the dependence of the solution on the small perturbations of the boundary with the Dirichlet and the Neumann data. Based on the fixed point iteration from the proof of the main result, we propose a numerical scheme and provide numerical examples. Parallelisation via the domain decomposition method is also given. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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