In this paper we deal with the null controllability for degenerate/singular parabolic systems memory terms. To aim, first prove property some auxiliary nonhomogeneous problems via new Carleman estimates their corresponding adjoint systems. Then, under a condition on kernels, using Kakutani's fixed point theorem, deduce results initial memory.

Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory. Abstract We obtain solutions of the nonlinear degenerate parabolic equation ∂ ρ ∂ t = div ρ ∇c ⋆ [ ∇ (F ′ (ρ) + V) ] as a steepest descent of an energy with respect to a convex cost functional. The method used here is variational. It requires less uniform convexity assumption than that imposed by Alt and ...

In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and initial condition. For the analysis these combine chaos expansion method from white noise concept very weak solutions. given equation introduce notion solution, prove existence uniqueness solution to corresponding value problem show its independence regularization...

We study a degenerate nonlinear parabolic equation with moving boundaries which arises in the study of the technique of contour enhancement in image processing. In order to obtain mass concentration at the contour, singular data must be imposed at the free boundary, leading to a non-standard free boundary problem. Our main results are: (i) the well-posedness for the singular problem, without mo...