Nonlinear Elliptic Dirichlet and No-Flux Boundary Value Problems
Loc Hoang Nguyen, Klaus Schmitt
TL;DR
This paper investigates the solvability of semilinear elliptic boundary value problems with No-Flux conditions by relating them to Dirichlet problems, focusing on gradient-dependent nonlinearities and extending to No-Flux scenarios.
Contribution
It establishes a connection between No-Flux and Dirichlet problems for elliptic equations with gradient-dependent nonlinearities, including extensions to No-Flux boundary conditions.
Findings
Solvability of No-Flux problems derived from Dirichlet problem solutions.
Extension of results to more general No-Flux boundary conditions.
Conditions under which solutions exist for gradient-dependent nonlinearities.
Abstract
This paper is devoted to establishing results for semilinear elliptic boundary value problems where the solvability of problems subject to {\it No Flux} boundary conditions follows from the solvability of related {\it Dirichlet} boundary value problems. Throughout it is assumed that the nonlinear perturbation terms are gradient dependent. An extension of \textit{No-Flux} problems is discussed, as well.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Differential Equations and Numerical Methods