A fixed point result with applications in the study of viscoplastic frictionless contact problems
By Mircea-Traian Sofonea, Cezar Avramescu, Andaluzia Cristina Matei. 2008
52 citations recorded by the source corpus.
Let $C(\mathbb R_+;X)$ denote the Frechet space of continuous functions defined on $\mathbb R_+=[0,\infty)$ with values on a real Banach space $(X,$ ||$\cdot$||$_X)$. We prove a fixed point theorem for operators $\Lambda:C(\mathbb R_+;X)\to C(\mathbb R_+;X)$ which satisfy a sequence of inequalities involving an integral term. Then we consider a mathematical model which describes the frictionless contact between a viscoplastic body and a deformable foundation. The process is quasistatic and is studied on the unbounded interval of time $[0,\infty)$. We provide the variational formulation of the problem, then we use the abstract fixed point theorem to prove the existence of a unique weak solution to the model. We complete our study with a regularity result.
Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/2b3907c8859bdfddae43b04f742abec327431131
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In Biomedical Engineering
In Computational Theory and Mathematics
In Mechanics of Materials
Citations in the corpus
- Fully history-dependent quasivariational inequalities in contact mechanics (2016, methodology): “The proof of Theorem 2 was carried out in several steps based on the fact that the space C(R+;X) can be organized as a Fréchet space with a convenient distance function (see [19] for details).”
- History-dependent quasi-variational inequalities arising in contact mechanics (2011, methodology): “Therefore, in order to prove the unique solvability of the quasi-variational inequalities, we use a different fixed point argument, obtained in [22].”