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Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

100%

Barnaś S.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2014

tom 34

nr 1

15-39

In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

72%

Barboteu M., Bartosz K., Kalita P.

International Journal of Applied Mathematics and Computer Science

2013

tom 23

nr 2

263-276

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 International Journal of Applied Mathematics and Computer Science

1 Barboteu M.

1 Barnaś S.

1 Bartosz K.

1 Kalita P.

1 2014

1 2013

Wyniki wyszukiwania

Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction