Abstract
We study existence and uniqueness of solutions to a class of quasilinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To this purpose some barrier functions are properly introduced and used.
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Punzo, F., Strani, M. Dirichlet Boundary Conditions for Degenerate and Singular Nonlinear Parabolic Equations. Potential Anal 47, 151–168 (2017). https://doi.org/10.1007/s11118-016-9611-9
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DOI: https://doi.org/10.1007/s11118-016-9611-9
Keywords
- Parabolic equations
- Dirichlet boundary conditions
- Barrier functions
- Sub– and supersolutions
- Comparison principle