Rational Approximation for a Quasilinear Parabolic Equation

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Existence of stable periodic solutions for quasilinear parabolic problems in the presence of well - ordered lower and upper - solutions ∗

We present existence and stability results for periodic solutions of quasilinear parabolic equation related to Leray-Lions’s type operators. To prove existence and localization, we use the penalty method; while for stability we use an approximation scheme.

Forward – backward stochastic di erential equations with nonsmooth coe cients

Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...

Computing Optimal Control with a Quasilinear Parabolic Partial Differential Equation

This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary optimality conditions for the considered problem are established. The computing optimal controls are helped to identify the unknown coefficien...

L1–framework for Continuous Dependence and Error Estimates for Quasilinear Anisotropic Degenerate Parabolic Equations

We develop a general L–framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach [9]. We apply our L–framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without t...