### 2001-13

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

Series: 2001-13, Preprints

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

Abstract:
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 $L^\infty(\R )$.

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