Research into contact problems continues to produce a rapidly
growing body of knowledge. Recognizing the need for a single,
concise source of information on models and analysis of contact
problems, accomplished experts Sofonea, Han, and Shillor carefully
selected several models and thoroughly study them in Analysis and
Approximation of Contact Problems with Adhesion or Damage. The book
describes very recent models of contact processes with adhesion or
damage along with their mathematical formulations, variational
analysis, and numerical analysis.
Following an introduction to modeling and functional and
numerical analysis, the book devotes individual chapters to models
involving adhesion and material damage, respectively, with each
chapter exploring a particular model. For each model, the authors
provide a variational formulation and establish the existence and
uniqueness of a weak solution. They study a fully discrete
approximation scheme that uses the finite element method to
discretize the spatial domain and finite differences for the time
derivatives. The final chapter summarizes the results, presents
bibliographic comments, and considers future directions in the
field.
Employing recent results on elliptic and evolutionary
variational inequalities, convex analysis, nonlinear equations with
monotone operators, and fixed points of operators, Analysis and
Approximation of Contact Problems with Adhesion or Damage places
these important tools and results at your fingertips in a unified,
accessible reference.
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