A. description In recent years several mathematical models in uid dynamics, materials science and plasticity have lead to fourth order nonlinear degenerate parabolic equations. We mention for example the lubrication approximation for thin viscous lms (cf. and models that describe dislocation densities in plasticity (cf. Gr un (1995)). Although there has been a considerable eeort to understand d...

We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations stochastic forcing, which heterogeneous (i.e., not space-translational invariant). A unified framework is established for the continuous dependence estimates, fractional BV regularity and well-posedness entropy solutions of equation. In particular, we establish equation in $L^p \cap N^{\kappa,1}$ $p\in (1,\inf...

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and singular potential. study case when potential arises at left endpoint weighted Dirichlet boundary control is located this point. get spectral decomposition suitable operator, defined in Sobolev space, involving Bessel functions their zeros, then we use moment method by Fattorini Russell to obtain...

it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

Abstract. We consider a system of degenerate parabolic equations modelling a thin film, consisting of two layers of immiscible Newtonian liquids, on a solid horizontal substrate. In addition, the model includes the presence of insoluble surfactants on both the free liquid-liquid and liquid-air interfaces, and the presence of both attractive and repulsive van der Waals forces in terms of the hei...