Electron. J. Differential Equations, Vol. 2016 (2016), No. 299, pp. 1-8.

Uniqueness of a very singular solution to nonlinear degenerate parabolic equations with absorption for Dirichlet boundary condition

Nguyen Anh Dao

We prove the existence and uniqueness of singular solutions (fundamental solution, very singular solution, and large solution) of quasilinear parabolic equations with absorption for Dirichlet boundary condition. We also show the short time behavior of singular solutions as t tends to 0.

Submitted August 14, 2016. Published November 25, 2016.
Math Subject Classifications: 35K65, 35K15.
Key Words: Degenerate parabolic equations; large solution; very singular solution; Dirac measure.

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Nguyen Anh Dao
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University, Ho Chi Minh City, Vietnam
email: daonguyenanh@tdt.edu.vn

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