Non-smooth variational problems and applications in mechanics

Abstract

Mathematical methods based on a variational approach are successfully used in a broad range of applications, especially those fields that are oriented on partial differential equations (PDEs). Our problem area addresses to a wide class of nonlinear problems described by all kinds of static, quasi-static and dynamic equations, inverse and optimal control problems, including shape and topology optimization. Within these directions, we focus but are not limited to multi-scale and non-flat geometries, singular and contact problems arising in solid and fluid mechanics, which are governed by complex systems of variational equations and inequalities.Whereas classical mathematical tools are not applicable here, we aim at non-standard existence and uniqueness analysis based on the primal and the dual variational formalism, at effective numerical methods for the solution of the underlying problems by use of approximation and asymptotic techniques including homogenization. In a broad scope, the theme issue objectives are directed towards advances that are recently attained in the mathematical theory of non-smooth variational problems. Methods of the non-smooth theory are supported by the physical consistency and reported in computer simulations for novel applications to engineering sciences.After successful publishing in 2022 in Philosophical Transactions of the Royal Society A of the theme issue 2236