We shall consider a model problem for the fully nonlinear parabolic equation u(t) + F(x, t, u, Du, epsilonD2u) = 0 and we study both the approximating degenerate second order problem and the related first order equation, obtained by the limit as epsilon --> 0. The strong convergence of the gradients is provided by semiconcavity unilateral bounds and by the supremum bounds of the gradients. In this way we find solutions in the class of viscosity solutions of Crandall and Lions.
APPROXIMATE SOLUTIONS TO 1ST AND 2ND-ORDER QUASI-LINEAR EVOLUTION-EQUATIONS VIA NONLINEAR VISCOSITY
PIERANGELO
1994-01-01
Abstract
We shall consider a model problem for the fully nonlinear parabolic equation u(t) + F(x, t, u, Du, epsilonD2u) = 0 and we study both the approximating degenerate second order problem and the related first order equation, obtained by the limit as epsilon --> 0. The strong convergence of the gradients is provided by semiconcavity unilateral bounds and by the supremum bounds of the gradients. In this way we find solutions in the class of viscosity solutions of Crandall and Lions.File in questo prodotto:
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