Variational-Hemivariational Inequalities with Applications
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Variational-Hemivariational Inequalities with Applications
Migorski, Stanislaw; Sofonea, Mircea
Taylor & Francis Ltd
12/2024
340
Dura
9781032587165
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I. Variational Problems in Solid Mechanics. 1. Elliptic Variational Inequalities. 1.1. Background on functional analysis. 1.2. Existence and uniqueness results. 1.3. Convergence results. 1.4. Optimal control. 1.5. Well-posedness results. 2. History-Dependent Operators. 2.1. Spaces of continuous functions. 2.2. Definitions and basic properties. 2.3. Fixed point properties. 2.4. History-dependent equations in Hilbert spaces. 2.5. Nonlinear implicit equations in Banach spaces. 2.6. History-dependent variational inequalities. 2.7. Relevant particular cases. 3. Displacement-Traction Problems in Solid Mechanics. 3.1. Modeling of displacement-traction problems. 3.2. A displacement-traction problem with locking materials. 3.3. One-dimensional elastic examples. 3.4. Two viscoelastic problems. 3.5. One-dimensional examples. 3.6. A viscoplastic problem. II. Variational-Hemivariational Inequalities. 4. Elements of Nonsmooth Analysis. 4.1. Monotone and pseudomonotone operators. 4.2. Bochner-Lebesgue spaces. 4.3. Subgradient of convex functions. 4.4. Subgradient in the sense of Clarke. 4.5. Mixed equilibrium problem. 4.6. Miscellaneous results. 5. Elliptic Variational-Hemivariational Inequalities. 5.1. An existence and uniqueness result. 5.2. Convergence results. 5.3. Optimal control. 5.4. Penalty methods. 5.5. Well-posedness results. 5.6. Relevant particular cases. 6. History-Dependent Variational-Hemivariational Inequalities. 6.1. An existence and uniqueness result. 6.2. Convergence results. 6.3. Optimal control. 6.4. A penalty method. 6.5. A well-posedness result. 6.6. Relevant particular cases. 7. Evolutionary Variational-Hemivariational Inequalities. 7.1. A class of inclusions with history-dependent operators. 7.2. History-dependent inequalities with unilateral constraints. 7.3. Constrainted differential variational-hemivariational inequalities. 7.4. Relevant particular cases. III. Applications to Contact Mechanics. 8. Static Contact Problems. 8.1. Modeling of static contact problems. 8.2. A contact problem with normal compliance. 8.3. A contact problem with unilateral constraints. 8.4. Convergence and optimal control results. 8.5. A contact problem for locking materials. 8.6. Convergence and optimal control results. 8.7. Penalty methods. 9. Time-Dependent and Quasistatic Contact Problems. 9.1. Physical setting and mathematical models. 9.2. Two time-dependent elastic contact problems. 9.3. A quasistatic viscoplastic contact problem. 9.4. A time-dependent viscoelastic contact problem. 9.5. Convergence and optimal control results. 9.6. A frictional viscoelastic contact problem. 9.7. A quasistatic contact problem with locking materials. 10. Dynamic Contact Problems. 10.1. Mathematical models of dynamic contact. 10.2. A viscoelastic contact problem with normal damped response. 10.3. A unilateral viscoelastic frictional contact problem. 10.4. A unilateral viscoplastic frictionless contact problem.
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nonlinear boundary value problems;Lipschitz function;history-dependent operators;Solid Mechanics;static, quasistatic and dynamic processes;Stanislaw Migrski
I. Variational Problems in Solid Mechanics. 1. Elliptic Variational Inequalities. 1.1. Background on functional analysis. 1.2. Existence and uniqueness results. 1.3. Convergence results. 1.4. Optimal control. 1.5. Well-posedness results. 2. History-Dependent Operators. 2.1. Spaces of continuous functions. 2.2. Definitions and basic properties. 2.3. Fixed point properties. 2.4. History-dependent equations in Hilbert spaces. 2.5. Nonlinear implicit equations in Banach spaces. 2.6. History-dependent variational inequalities. 2.7. Relevant particular cases. 3. Displacement-Traction Problems in Solid Mechanics. 3.1. Modeling of displacement-traction problems. 3.2. A displacement-traction problem with locking materials. 3.3. One-dimensional elastic examples. 3.4. Two viscoelastic problems. 3.5. One-dimensional examples. 3.6. A viscoplastic problem. II. Variational-Hemivariational Inequalities. 4. Elements of Nonsmooth Analysis. 4.1. Monotone and pseudomonotone operators. 4.2. Bochner-Lebesgue spaces. 4.3. Subgradient of convex functions. 4.4. Subgradient in the sense of Clarke. 4.5. Mixed equilibrium problem. 4.6. Miscellaneous results. 5. Elliptic Variational-Hemivariational Inequalities. 5.1. An existence and uniqueness result. 5.2. Convergence results. 5.3. Optimal control. 5.4. Penalty methods. 5.5. Well-posedness results. 5.6. Relevant particular cases. 6. History-Dependent Variational-Hemivariational Inequalities. 6.1. An existence and uniqueness result. 6.2. Convergence results. 6.3. Optimal control. 6.4. A penalty method. 6.5. A well-posedness result. 6.6. Relevant particular cases. 7. Evolutionary Variational-Hemivariational Inequalities. 7.1. A class of inclusions with history-dependent operators. 7.2. History-dependent inequalities with unilateral constraints. 7.3. Constrainted differential variational-hemivariational inequalities. 7.4. Relevant particular cases. III. Applications to Contact Mechanics. 8. Static Contact Problems. 8.1. Modeling of static contact problems. 8.2. A contact problem with normal compliance. 8.3. A contact problem with unilateral constraints. 8.4. Convergence and optimal control results. 8.5. A contact problem for locking materials. 8.6. Convergence and optimal control results. 8.7. Penalty methods. 9. Time-Dependent and Quasistatic Contact Problems. 9.1. Physical setting and mathematical models. 9.2. Two time-dependent elastic contact problems. 9.3. A quasistatic viscoplastic contact problem. 9.4. A time-dependent viscoelastic contact problem. 9.5. Convergence and optimal control results. 9.6. A frictional viscoelastic contact problem. 9.7. A quasistatic contact problem with locking materials. 10. Dynamic Contact Problems. 10.1. Mathematical models of dynamic contact. 10.2. A viscoelastic contact problem with normal damped response. 10.3. A unilateral viscoelastic frictional contact problem. 10.4. A unilateral viscoplastic frictionless contact problem.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
