A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION

Title & Authors
A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION
Fang, Zhong Bo;

Abstract
We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation: $\small{[\mid(w^m)]$ satisfying a specific decay rate: $\small{lim_{r\rightarrow\infty}\;r^{\alpha/\beta}w(r)}$ = 0 with $\small{\alpha}$ := (p - 1)/[pd-(m+1)(p-1)] and $\small{\beta}$:= [q-m(p-1)]/[pd-(m+1)(p-1)]. Here m(p-1) > 1 and m(p - 1) < q < (m+1)(p-1). Such a solution arises naturally when we study a very singular solution for a doubly degenerate equation with nonlinear convection: $\small{u_t\;=\;[\mid(u^m)_x\mid^{p-2}(u^m)_x]_x\;+\;(u^q)x}$ defined on the half line.
Keywords
very singular solution;existence;uniqueness;asymptotic behavior;
Language
English
Cited by
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