01-13
Existence and Uniqueness of Solutions for a Non-uniformly Parabolic Equation
Preprint series: 01-13, Preprints
- MSC:
- 35K55 Nonlinear PDE of parabolic type
- 35B65 Smoothness/regularity of solutions of PDE
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
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