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Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Complete quenching phenomenon and instantaneous shrinking of support of solutions of degenerate parabolic equations with nonlinear singular absorption
Part of
- Parabolic equations and systems
- Partial differential equations
Nguyen Anh Dao, Jesus Ildefonso Díaz, Huynh Van Kha
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 5 / October 2019

Published online by Cambridge University Press:

17 January 2019, pp. 1323-1346

Print publication:

October 2019
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This paper deals with nonnegative solutions of the one-dimensional degenerate parabolic equations with zero homogeneous Dirichlet boundary condition. To obtain an existence result, we prove a sharp estimate for |ux|. Besides, we investigate the qualitative behaviours of nonnegative solutions such as the quenching phenomenon, and the finite speed of propagation. Our results of the Dirichlet problem are also extended to the associated Cauchy problem on the whole domain ℝ. In addition, we also consider the instantaneous shrinking of compact support of nonnegative solutions.