The Cauchy Problem of the Porous Medium Equation with Absorption

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Abstract

In this paper we study the existence of solution for the following Cauchy problem {u_t = Δu^m - u^p u(x,0) = u_0(x) We show how the growth condition of initial trace is determined by the absorption.

Keywords:

Existence of solution; Cauchy problem; porous media equation
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The Cauchy Problem of the Porous Medium Equation with Absorption. (1994). Journal of Partial Differential Equations, 7(3), 231-247. https://www.global-sci.com/index.php/jpde/article/view/3774