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

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.

Keywords:

• Cauchy problem
• degenerate parabolic equations
• nonpower nonlinearity
• long-time behaviour

AMS Subject Classifications:

• Primary: 35B45
• Secondary: 35B45
• 35K55
• 35K59
• 35K65

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.