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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 18
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Research Article

Long-time behaviour of the solution to the Cauchy problem for degenerate parabolic equations with nonpower nonlinearities

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Pages 6485-6494 | Received 08 Feb 2021, Accepted 27 Apr 2021, Published online: 21 May 2021
 

Abstract

We prove the qualitative decay in time estimate of supremum norm of the nonnegative solution to the Cauchy problem for quasilinear degenerate parabolic equations with nonpower nonlinearity. The result obtained is given in terms of the initial data mass and nonlinearity structure. In particular, if the nonlinearity of the equation is power like, then our result coincides with well-known optimal bound.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research is supported by RUDN university Project 5-100.

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