Zurück zu den Preprints des Jahres 2001


Existence and Uniqueness of Solutions for a Non-uniformly Parabolic Equation

by Wang, J., Warnecke, G..

Series: 2001-13, Preprints

35K55 Nonlinear parabolic equations
35B65 Smoothness and regularity of solutions

In this paper we study a generalized Burgers
equation $u_t+(u^2)_x=tu_{xx}$, which is a non-uniformly parabolic
equation for $t>0$. We show the existence and uniqueness of classical
solutions to the initial value problem of the generalized Burgers
equation with rough initial data belonging to $L^\infty(\R )$.

Non-uniformly parabolic equation, existence, uniqueness, classical solutions