Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations

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...

Probabilistic Interpretation of a System of Quasilinear Parabolic Pdes

Using a forward– backward stochastic differential equations (FBSDE) associated to a transmutation process driven by a finite sequence of Poisson processes, we obtain a probabilistic interpretation for a non-degenerate system of quasilinear parabolic partial differential equations (PDEs). The novetly is that the linear second order differential operator is different on each line of the system.

Quasilinear Parabolic Stochastic Partial Differential Equations: Existence, Uniqueness

In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally monotone.

Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case

In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic solution and develop a well-posedness theory that includes also an L1-contraction property. In comparison to the previous works of the authors concerning stochastic...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption