In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with locally distributed control. We first derive result nonhomogeneous heat via new Carleman estimates weighted time functions that do not blow up at t= 0. Then is successfully used classical fixed point to obtain initial system.

We study a seawater intrusion problem in a confined aquifer. This process can be formulated as a coupled system of partial differential equations which includes an elliptic and a degenerate parabolic equation. Existence results of weak solutions, under realistic assumptions, are established through time discretization combined with parabolic regularization.

We prove that a sequence of quasi-solutions to non-degenerate degenerate parabolic equations with rough coefficients is strongly Lloc-precompact. The result is obtained using the H-measures and a new concept of quasihomogeneity. A consequence of the precompactness is existence of a weak solution to the equation under consideration.

This paper is devoted to the mathematical analysis of a degenerate nonlinear parabolic equation. This kind of equations stems either from the modeling of a compressible two phase flow in porous media or from the modeling of a chemotaxis-fluid process. In the degenerate equation, the strong nonlinearities are technically difficult to be controlled by the degenerate dissipative term because the e...

Nonlinear degenerate parabolic-hyperbolic equations are one of the most important classes of nonlinear partial differential equations. Nonlinearity and degeneracy are two main features of these equations and yield several striking phenomena that require new mathematical ideas, approaches, and theories. On the other hand, because of the importance of these equations in applications, there is a l...

In this article, we study the existence and the upper semicontinuity with respect to the nonlinearity and the shape of the domain of global attractors for a semilinear degenerate parabolic equation involving the Grushin operator.

We study the interior regularity properties of the solutions to the degenerate parabolic equation, ∆xu+ b∂yu− ∂tu = f, (x, y, t) ∈ R × R× R, which arises in mathematical finance and in the theory of diffusion processes.

This paper concerns the weak solutions to a Cauchy problem in RN for a degenerate nonlinear parabolic equation. We obtain the Hölder regularity of the weak solutions to this problem.

We prove well-posedness for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = Cγ ρ for γ > 1. The physical vacuum singularity requires the sound speed c to go to zero as the square-root of the distance to the moving boundary, and thus creates a degenerate and characteristic hyperbolic free-boundary system wherein t...