Abstract
This paper presents a full classification of the short-time behavior of the interfaces in the Cauchy problem for the nonlinear second order degenerate parabolic PDE
with nonnegative initial function \(u_0\) such that
where \(m>1, C,\alpha , \beta >0, b \in {\mathbb {R}}\). Interface surface \(t=\eta (x)\) may shrink, expand or remain stationary depending on the relative strength of the diffusion and reaction terms near the boundary of support, expressed in terms of the parameters \(m,\beta , \alpha , sign\ b\) and C. In all cases we prove explicit formula for the interface asymptotics, and local solution near the interface.
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Appendix
Appendix
Here we bring explicit values of the constants used in Sects. 2 and 5 .
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Abdulla, U.G., Abuweden, A. Interface development for the nonlinear degenerate multidimensional reaction–diffusion equations. Nonlinear Differ. Equ. Appl. 27, 3 (2020). https://doi.org/10.1007/s00030-019-0606-2
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DOI: https://doi.org/10.1007/s00030-019-0606-2
Keywords
- Nonlinear degenerate parabolic equations
- Reaction–diffusion equations
- Interfaces
- Nonlinear diffusion
- Weak solutions
- Comparison theorem