Investigation of weak solutions of double nonlinear parabolic equation in non-divergence form with source term

Abstract

In this study, we explore the positive solution to a Cauchy problem in  of the diffusive equation: considering initial data that is neither trivial or negative. Here  are the given parameters. We prove that  is the critical Fujita exponent. That is, if , then every positive solution blows up in finite time, but for , there exist both global and non-global solutions to the problem. The findings of this paper include all previously published results by other authors at specific numerical parameter values. Analysis of self-similar analysis and numerical evaluation of solutions are discussed.