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Uniqueness and existence of viscosity solutions under a degenerate dynamic boundary condition
| Title: | Uniqueness and existence of viscosity solutions under a degenerate dynamic boundary condition |
| Authors: | Hamamuki, Nao Browse this author |
| Keywords: | degenerate dynamic boundary condition | | comparison principle | | viscosity solutions |
| Issue Date: | 2-Apr-2020 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1131 |
| Start Page: | 1 |
| End Page: | 36 |
| Abstract: | We consider the initial boundary value problem for a fully-nonlinear parabolic equation in a half space. The boundary condition we study is a degenerate one in the sense that it does not depend on the normal derivative on the boundary. A typical example is a stationary boundary condition prescribing the value of the time derivative of the unknown function. Our setting also covers the classical Dirichlet boundary condition. We establish a comparison principle for a viscosity sub- and supersolution under a weak continuity assumption on the solutions on the boundary. We also prove existence of solutions and give some examples of solutions under several boundary conditions. We show among other things that, in the sense of viscosity solutions, the stationary boundary condition can be different from the Dirichlet boundary condition which is obtained by integrating the stationary condition. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/77215 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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