Liu Zhenhai

On the identification of coefficients of semilinear parabolic equations

In this paper, a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered. General theorems on existence are proved inL1 setting. A necessary condition is given for the solution of the parameter estimation problem.

On quasilinear elliptic hemivariational inequalities

In the present paper, quasilinear elliptic hemivariational inequalities as a generalization to nonconvex functionals of the elliptic variational inequalities are studied. This extension is strongly motivated by various problems in mechanics. By using the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, the existence of solutions in proved.

On the degree theory for multivalued (S+) type mappings

This paper is to generalize the results of Zhang and Chen[1]. We construct a topological degree for a class of mappings of the form F=L+S where L is closed densely defined maximal monotones operator and S is a nonlinear multivalued map of class (S+) with respect to the domain of L.

On Quasilinear Elliptic Hemivariational Inequalities of Higher Order

In this paper we deal with quasilinear elliptic hemivariational inequalities of higher order as generalizations of elliptic variational inequalities of higher order to nonconvex functionals. This extension is strongly motivated by various problems in mechanics. Using the notion of the generalized gradient of Clarke, existence results of solutions have been obtained.

Existence for implicit differential equations with nonmonotone perturbations

This paper is devoted to the existence of solutions for a class of implicit Cauchy problems. The main tools in our study will be a convergent approximation procedure and the theory of pseudomonotone perturbations of maximal monotone mappings.

A CLASS OF PARABOLIC HEMIVARIATIONAL INEQUALITIES

Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed. This extension is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, it is proved there exists at least one solution.

Existence of solutions for degenerate quasilinear parabolic equations of higher order

In the paper, existence results for degenerate parabolic boundary value problems of higher order are proved. The weak solution is sought in a suitable weighted Sobolev space by using the generalized degree theory.

A class of quasilinear elliptic hemivariational inequalities

In this paper, we shall deal with quasilinear elliptic hemivariational inequalities. By the use of the theory of multivalued pseudomonotone mappings, we will prove the existence of solutions.

On degenerate quasilinear parabolic equations of higher order

In the paper existence results for degenerate quasilinear parabolic initial boundary value problems of higher order are proved. The weak solution is sought in a suitable weighted Sobolev space using the generalized degree theory.