The dissertation deals with second order nonlinear evolution inclusions, hyperbolic hemivariation... more The dissertation deals with second order nonlinear evolution inclusions, hyperbolic hemivariational inequalities and their applications. First, we study a class of the evolution inclusions involving a Volterra integral operator and considered within the framework of an evolution triple of spaces. Combining a surjectivity result for multivalued pseudomonotone operators and the Banach Contraction Principle, we deliver a result on the unique solvability of the Cauchy problem for the inclusion. We also provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Next, we consider a class of hyperbolic hemivariational inequalities and embed these problems into a class of evolution inclusions with the multivalued term generated by the generalized Clarke subdifferential for nonconvex and nonsmooth superpotentials. Finally, we study a dynamic frictional contact problem of viscoelasticity with a general constitutive la...
Zeitschrift für Analysis und ihre Anwendungen, 2015
This work studies a model for quasistatic frictional contact between a viscoelastic body and a re... more This work studies a model for quasistatic frictional contact between a viscoelastic body and a reactive foundation. The constitutive law is assumed to be nonlinear and contains damage effects modeled by a parabolic differential inclusion. Contact is described by the normal compliance condition and a subdifferential frictional condition. A variational-hemivariational formulation of the problem is provided and the existence and uniqueness of its solution is proved. The proof is based on a surjectivity result for pseudomonotone coercive operators and a fixed point argument.
A. Kulig, S. Migorski, Solvability and Continuous Dependence Results for Second Order Nonlinear Evolution Inclusions with a Volterra-type Operator, Nonlinear Analysis Theory, Methods and Applications, 75 (2012), 4729-4746
The paper deals with second order nonlinear evolution inclusions and their applications. First, w... more The paper deals with second order nonlinear evolution inclusions and their applications. First, we study an evolution inclusion involving Volterra-type integral operator which is considered within the framework of an evolution triple of spaces. We provide a result on the unique solvability of the Cauchy problem for the inclusion. Next, we examine a dynamic frictional contact problem of viscoelasticity for materials with long memory and derive a weak formulation of the model in the form of a hemivariational inequality. Then, we embed the hemivariational inequality into a class of second order evolution inclusions involving Volterra-type integral operator and indicate how the result on evolution inclusion is applicable to the model of the contact problem. We conclude with examples of the subdifferential boundary conditions for different types of frictional contact.
Nonlinear Analysis Theory Methods Applications, Sep 1, 2012
The paper deals with second order nonlinear evolution inclusions and their applications. We study... more The paper deals with second order nonlinear evolution inclusions and their applications. We study evolution inclusions involving a Volterra-type integral operator, which are considered within the framework of an evolution triple of spaces. First, we deliver a result on the unique solvability of the Cauchy problem for the inclusion by combining a surjectivity result for multivalued pseudomonotone operators and the Banach contraction principle. Next, we provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Finally, we consider a dynamic frictional contact problem of viscoelasticity for materials with long memory and indicate how the result on evolution inclusion is applicable to the model of the contact problem.
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Papers by Anna Kulig