# The Existence and Asymptotic Behaviour of Similarity Solutions to a Quasilinear Parabolic Equation

Chapter

## Abstract

In this paper we study the existence and properties of similarity solutions which blow-up in finite time, of the nonlinear parabolic equation where 0 < α < 1, p > 1. This is a transformation of the well-known porous media equation which can be regarded as to describe the propagation of thermal perturbations in a medium with a nonlinear heat conduction coefficient and a heat source term, depending on the temperature. Indeed, let *v* be a solution of porous media equation

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