Smoothing of quasilinear parabolic operators and applications to forward-backward stochastic systems. (English) Zbl 1103.35041

Guatteri, Giuseppina; Lunardi, Alessandra

Adv. Differ. Equ. 10, No. 1, 65-88 (2005).

The authors study the Cauchy problem for a certain quasilinear parabolic equation with quadratic nonlinearity in the gradient and with Hölder-continuous, not necessarily differentiable, initial datum, under suitable regularity and growth assumptions on the nonlinear functions involved therein. An application to stochastic forward-backward systems is also discussed.

Reviewer: B. G. Pachpatte (Aurangabad)

MSC:

35K55	Nonlinear parabolic equations
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
35K15	Initial value problems for second-order parabolic equations

Keywords:

quadratic nonlinearity