On a dynamic boundary condition for singular degenerate parabolic equations in a half space

• Giga Yoshikazu

• Hamamuki Nao

Abstract

We consider the initial value problem for a fully-nonlinear degenerate parabolic equation with a dynamic boundary condition in a half space. Our setting includes geometric equations with singularity such as the level-set mean curvature flow equation. We establish a comparison principle for a viscosity sub- and supersolution. We also prove existence of solutions and Lipschitz regularity of the unique solution. Moreover, relation to other types of boundary conditions is investigated by studying the asymptotic behavior of the solution with respect to a coefficient of the dynamic boundary condition.

Journal

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 1110 1-38, 2018-04-28

  Department of Mathematics, Hokkaido University

Keywords

• dynamic boundary condition
• geometric equations
• comparison principle
• viscosity solutions

Details

• CRID: 1390290699772206464
• NII Article ID: 120006462293
• DOI: 10.14943/84298
• HANDLE: 2115/70072
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
• Abstract License Flag: Allowed