A class of elliptic mixed boundary value problems with (p, q)-Laplacian: existence, comparison and optimal control
A class of elliptic mixed boundary value problems with (p, q)-Laplacian: existence, comparison and optimal control
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DOI：
10.1007/s00033-022-01789-7
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Van Thien Nguyen
中科院分区：
文献类型：
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作者：
Shengda Zeng;Stanislaw Migorski;Domingo A. Tarzia;Lang Zou;Van Thien Nguyen
The paper deals with two nonlinear elliptic equations with (p, q)-Laplacian and the Dirichlet–Neumann–Dirichlet.(DND) boundary conditions, and Dirichlet–Neumann–Neumann (DNN) boundary conditions, respectively. Under mild.hypotheses, we prove the unique weak solvability of the elliptic mixed boundary value problems. Then, a comparison and a.monotonicity results for the solutions of elliptic mixed boundary value problems are established. We examine a convergence.result which shows that the solution of (DND) can be approached by the solution of (DNN). Moreover, two optimal control.problems governed by (DND) and (DNN), respectively, are considered, and an existence result for optimal control problems.is obtained. Finally, we provide a result on asymptotic behavior of optimal controls and system states, when a parameter.tends to infinity.
