We deal with systems of PDEs, arising in mean field games theory, where viscous Hamilton–
Jacobi and Fokker–Planck equations are coupled in a forward-backward structure. We …

We first introduce, using a functional approach, the notion of capacity related to the parabolic
p-Laplace operator. Then we prove a decomposition theorem for measures (in space and …

We consider the nonlinear heat equation (with Leray-Lions operators) on an open bounded
subset of RN with Dirichlet homogeneous boundary conditions. The initial condition is in L 1 …

We introduce function spaces for the treatment of parabolic equations with variable
exponents by means of the theory of monotone operators. We generalize classical results …

In this paper we study a novel class of inverse problems for parabolic variational–
hemivariational inequalities with a unilateral constraint. A theorem on the well-posedness for …

We study here the approximation by a finite-volume scheme of a heat equation forced by a
Lipschitz continuous multiplicative noise in the sense of Itô. More precisely, we consider a …

We study a finite volume discretization of a strongly coupled elliptic-parabolic PDE system
describing miscible displacement in a porous medium. We discretize each equation by a …

We develop a general framework for the analysis of approximations to stochastic scalar
conservation laws. Our aim is to prove, under minimal consistency properties and bounds …

An exponential turnpike property for a semilinear control problem is proved. The state-target
is assumed to be small, whereas the initial datum can be arbitrary. Turnpike results are also …

We present a unified framework for goal-oriented estimates for elliptic and parabolic
problems that combines the dual-weighted residual method with equilibrated flux and …