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On the mixed boundary value problem for semilinear elliptic equations

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  • Mišur, Marin

Abstract

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.

Suggested Citation

  • Mišur, Marin, 2021. "On the mixed boundary value problem for semilinear elliptic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 162-177.
    • Handle: RePEc:eee:matcom:v:179:y:2021:i:c:p:162-177
    DOI: 10.1016/j.matcom.2020.08.004
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