The two obstacle problem for the parabolic biharmonic equation
Matteo Novaga, Shinya Okabe
TL;DR
This paper studies a two obstacle problem for the parabolic biharmonic equation, establishing long-term existence of solutions and analyzing their regularity in a bounded domain.
Contribution
It introduces a novel approach to solving the two obstacle problem for the parabolic biharmonic equation and proves long-time existence using an implicit time discretization scheme.
Findings
Long-time existence of solutions is established.
Regularity properties of solutions are investigated.
The implicit time discretization scheme is effective for this problem.
Abstract
We consider a two obstacle problem for the parabolic biharmonic equation in a bounded domain. We prove long time existence of solutions via an implicit time discretization scheme, and we investigate the regularity properties of solutions.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Numerical methods in inverse problems