We prove here an existence result for solutions for a parabolic equation, with non local coefficients arising in image processing. An image is a bounded function u : D → R defined on a rectangular region D. If the function u is not regular, the image is noisy and it is not possible to use it directly in applications, but is necessary to smooth it by means of a nonlinear evolution problem, with ...

This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that vanish on the degeneracy set, together with their conormal derivative, are identically equal to zero. An approximate controllability result for weakly degenerate parabolic equations under Dirichlet boundary c...

In the rst part of this paper, the mathematical analysis is presented in detail for the single-phase, miscible displacement of one uid by another in a porous medium. It is shown that initial boundary value problems with various boundary conditions for this miscible displacement possess a weak solution under physically reasonable hypotheses on the data. Then in the second part of this paper, it ...

Abstract. The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton–Jacobi– Bellman (HJB) equation. A nonlinear parabolic evolution equation is then proposed as a continuous time continuous state space analog of White’s ‘relative value iteration’ ...