Monotonie bei Nichtlinearen Stefan-Problemen

Abstract

In his paper [2] G. W. Evans proved existence and uniqueness of the solution of the Stefan-Problem

$$ \begin{array}{*{20}{c}} {{{u}_{{xx}}} - {{u}_{t}} = 0} & , & {0 < x < s\left( t \right)} & , \\ {u\left( {s\left( t \right),t} \right) = 0} & , & {s\left( 0 \right) = 0} & , \\ {{{u}_{x}}\left( {0,t} \right) = - 1} & , & {} & {} \\ {\dot{s}\left( t \right) = - {{u}_{x}}\left( {s\left( t \right),t} \right)} & {for} & {t > 0} & . \\ \end{array} $$