## Grant IAA100750802
1.1.2008 - 31.12.2011

Grantor: Grant Agency of Czech Academy of Sciences

### Nonsmooth and set-valued analysis in mechanics and thermomechanics

Nonsmooth and set-valued analysis represent powerful mathematical tools which make possible to build and to treat complex models. This includes solvability of problems, stability and sensitivity of their solutions with respect to model data, their dependence on possible control variables, and numerical solution. In the proposed project, we plan to apply these tools to six closely related problem areas. Specifically, we will be dealing with rate-independent processes, anisothermal processes, generalized equations with nonpolyhedral multifunctions, various types of contact problems (static and dynamic) and free boundary problems. The planned research encompasses both answers to deep theoretical questions (e.g. investigation of thermally coupled plasticity) as well as the development of new numerical techniques and solution of difficult non-academic test problems (e.g. shape optimization in contact problems with Coulomb friction with a solution-dependent coefficient of friction).