Tomáš Ligurský
Katedra matematické analýzy a aplikací matematiky
Přírodovědecká fakulta Univerzity Palackého v Olomouci

Parameter-dependent piecewise-smooth problems: theoretical analysis, numerical continuation and an application in contact problems with friction
A local study of solution branching will be presented in a class of piecewise-smooth steady-state problems for which the regions of smooth behaviour permit analytical expressions. A system of piecewise-linear equations will be derived for determining the tangential directions of curves emanating from points of non-smoothness under certain non-degeneracy conditions. The simplest cases of this system will be analysed and the most probable branching scenarios will be described. A technique for numerical continuation of solution curves will be developed. Application of the general frame to discretised plane contact problems with Coulomb friction will be explained. Finally, numerical examples will be shown.