Lower semicontinuous differential inclusions. One-sided Lipschitz approach

Semilinear Parabolic Differential Inclusions with One-sided Lipschitz Nonlinearities

We present an existence result for a partial differential inclusion with linear parabolic principal part and relaxed one-sided Lipschitz multivalued nonlinearity in the framework of Gelfand triples. Our study uses discretizations of the differential inclusion by a Galerkin scheme, which is compatible with a conforming finite element method, and we analyze convergence properties of the discrete ...

Lower Semicontinuous Differential Inclusions with State Constrains 1

The main purpose of the present paper is to impose onesided Lipschitz condition for differential inclusions on a closed and convex domain of a uniformly convex Banach space. Both differential inclusions with almost upper demicontinuous and almost lower semicontinuous right–hand sides are considered. The existence theorems are proved and it is shown that the set of solutions is connected. AMS Ma...

Nonlocal Conditions for Lower Semicontinuous Parabolic Inclusions

Let Ω be an open bounded domain in N , N ≥ 2, with a smooth boundary ∂Ω. We denote the norm usually the Euclidean norm of x ∈ Ω by ‖x‖. Let T be a positive real number. Set QT Ω × 0, T and ΓT ∂Ω × 0, T . For u : D → we denote its partial derivatives when they exist by ut ∂u/∂t, uxi ∂u/∂xi, uxixj ∂ u/∂xi∂xj , i, j 1, . . . ,N. Let X C QT denote the Banach space of continuous functions u : QT → ,...

An Iterative Method for Solving Relaxed One-Sided Lipschitz Algebraic Inclusions

An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is improved. This enhanced solvability result allows the design of a robust iterative method for the numerical solution of the algebraic inclusion. Sharp error estimates for this method, illustrative analytic examples and a numerical example are provided.

Waveform Iteration and One-sided Lipschitz Conditions