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.