This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.
Abstract In this paper, we introduce a modified Landweber iteration to solve the sideways parabolic equation, which is an inverse heat conduction problem （IHCP） in the quarter plane and is severely ill-posed. We shall show that our method is of optimal order under both a priori and a posteriori stopping rule. Furthermore, if we use the discrepancy principle we can avoid the selection of the a priori bound. Numerical examples show that the computation effect is satisfactory.
We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.
This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.
This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB（u）/dt ＋ A（u） f, v0 ∈ B（u）（0）, where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.
