Academic Journals Database
Disseminating quality controlled scientific knowledge

Good Solutions of Fully Nonlinear Parabolic Equations

Author(s): Tran Duc Van | Tran Van Bang

Journal: Selçuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 3;
Issue: 1;
Start page: 100;
Date: 2002;
Original page

Keywords: L^{p}-viscosity solutions | good solutions | strong solutions | fully nonlinear parabolic equations.

In this paper, we introduce the notion of a "good" solution of a fully nonlinear parabolic equation and show that "good" solutions are equivalent to L^{p} -viscosity solutions of such equations. The results here generalize the ones in [8] about "good" solutions of fully nonlinear elliptic equations. We give here an explicit construction of parabolic equations with L^{p} –strong solutions that approximate some nonlinear parabolic equation and its L^{p} -viscosity solution.