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Nonlinear Inclusions and Hemivariational Inequalities

Part of the Advances in Mechanics and Mathematics Book Series (volume 26)

DOI: 10.1007/978-1-4614-4232-5

ISBN: 978-1-4614-4231-8

Publisher: Springer New York - Springer Journals

Jun 14, 2012

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Preliminaries

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 3 –22

[In this chapter we present preliminary material from functional analysis which will be used subsequently. The results are stated without proofs, since they are standard and can be found in many references. For the convenience of the reader we summarize definitions and results on normed spaces,...
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Function Spaces

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 23 –49

[In this chapter we introduce function spaces that will be relevant to the subsequent developments in this monograph. The function spaces to be discussed include spaces of continuous and continuously differentiable functions, smooth functions, Lebesgue and Sobolev spaces, associated with an open...
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Elements of Nonlinear Analysis

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 51 –91

[In this chapter we present basic material on the set-valued mappings, nonsmooth analysis, subdifferential calculus, and operators of monotone type. For set-valued mappings we concentrate on measurability and continuity issues which we need in subsequent chapters. The section on nonsmooth...
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Stationary Inclusions and Hemivariational Inequalities

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 95 –120

[In this chapter we study stationary operator inclusions, i.e., inclusions in which the derivatives of the unknown with respect to the time variable are not involved. We start with a basic existence result for abstract operator inclusions. Then we use it in order to prove the existence of...
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Evolutionary Inclusions and Hemivariational Inequalities

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 121 –171

[In this chapter we study evolutionary inclusions of second order. These are multivalued relations which involve the second-order time derivative of the unknown. We start with a basic existence result for such inclusions. Then we provide results on existence and uniqueness of solutions to...
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Modeling of Contact Problems

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 175 –199

[In this chapter we deal with the mathematical modeling of the processes of contact between a deformable body and a foundation. We present the physical setting, the variables which determine the state of the system, the balance equations, the material’s behavior which is reflected in the...
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Analysis of Static Contact Problems

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 201 –240

[In this chapter we illustrate the use of the abstract results obtained in Chap. 4, in the study of three representative static frictional contact problems for deformable bodies. In the first two problems we model the material’s behavior with a nonlinear elastic constitutive law and with a...
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Analysis of Dynamic Contact Problems

Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea

Pages: 241 –265

[In this chapter we apply the abstract results of Chap. 5 in the study of three dynamic frictional contact problems. In the first two problems we model the material’s behavior with a nonlinear viscoelastic constitutive laws with short and long memory, respectively. In the third problem the body...

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