Advances in Variational and Hemivariational Inequalities: Theory, Numerical Analysis, and Applications (Advances in Mechanics and Mathematics Book 33)

This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities. Highlighting Recent Advances In Variational And Hemivariational Inequalities With An Emphasis On Theory, Numerical Analysis And Applications, This Volume Serves As An Indispensable Resource To Graduate Students And Researchers Interested In The Latest Results From Recognized Scholars In This Relatively Young And Rapidly-growing Field. Particularly, Readers Will Find That The Volume’s Results And Analysis Present Valuable Insights Into The Fields Of Pure And Applied Mathematics, As Well As Civil, Aeronautical, And Mechanical Engineering. Researchers And Students Will Find New Results On Well Posedness To Stationary And Evolutionary Inequalities And Their Rigorous Proofs. In Addition To Results On Modeling And Abstract Problems, The Book Contains New Results On The Numerical Methods For Variational And Hemivariational Inequalities. Finally, The Applications Presented Illustrate The Use Of These Results In The Study Of Miscellaneous Mathematical Models Which Describe The Contact Between Deformable Bodies And A Foundation. This Includes The Modelling, The Variational And The Numerical Analysis Of The Corresponding Contact Processes. Furthermore, It Can Be Used As Supplementary Reading Material For Advanced Specialized Courses In Mathematical Modeling For Students With A Strong Background Knowledge On Nonlinear Analysis, Numerical Analysis, Partial Differential Equations, And Mechanics Of Continua. Bifurcation Phenomena For Parametric Nonlinear Elliptic Hemivariational Inequalities -- Evolutionary Inclusions And Hemivariational Inequalities -- Location Results For Variational-hemivariational Inequalities -- Nonconvex Variational Inequalities -- Numerical Methods For Evolution Hemivariational Inequalities -- Some Extragradient Algorithms For Variational Inequalities -- Proximal Methods For The Elastography Inverse Problem Of Tumor Identification Using An Equation Error Approach -- Discontinuous Galerkin Methods For An Elliptic Variational Inequality Of 4th-order -- Dynamic Gao Beam In Contact With A Reactive Or Rigid Foundation -- A Hyperelastic Dynamic Frictional Contact Model With Energy-consistent Properties -- A Non-clamped Frictional Contact Problem With Normal Compliance -- On Large Time Asymptotics For Two Classes Of Contact Problems -- Hemivariational Inequalities For Dynamic Elastic-viscoplastic Contact Problems -- Two History-dependent Contact Problems. Edited By Weimin Han, Stanisław Migórski, Mircea Sofonea. Highlighting recent advances in variational and hemivariational inequalities with an emphasis on theory, numerical analysis and applications, this volume serves as an indispensable resource to graduate students and researchers interested in the latest results from recognized scholars in this relatively young and rapidly-growing field. Particularly, readers will find that the volumeĺls results and analysis present valuable insights into the fields of pure and applied mathematics, as well as civil, aeronautical, and mechanical engineering. Researchers and students will find new results on well posedness to stationary and evolutionary inequalities and their rigorous proofs. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities. Finally, the applications presented illustrate the use of these results in the study of miscellaneous mathematical models which describe the contact between deformable bodies and a foundation. This includes the modelling, the variational and the numerical analysis of the corresponding contact processes. Furthermore, it can be used as supplementary reading material for advanced specialized courses in mathematical modeling for students with a strong background knowledge on nonlinear analysis, numerical analysis, partial differential equations, and mechanics of continua Front Matter....Pages i-xiii Front Matter....Pages 1-1 Bifurcation Phenomena for Parametric Nonlinear Elliptic Hemivariational Inequalities....Pages 3-37 Evolutionary Inclusions and Hemivariational Inequalities....Pages 39-64 Location Results for Variational–Hemivariational Inequalities....Pages 65-88 Nonconvex Variational Inequalities....Pages 89-108 Front Matter....Pages 109-109 Numerical Methods for Evolution Hemivariational Inequalities....Pages 111-144 Some Extragradient Algorithms for Variational Inequalities....Pages 145-171 Proximal Methods for the Elastography Inverse Problem of Tumor Identification Using an Equation Error Approach....Pages 173-197 Discontinuous Galerkin Methods for an Elliptic Variational Inequality of Fourth-Order....Pages 199-222 Front Matter....Pages 223-223 Dynamic Gao Beam in Contact with a Reactive or Rigid Foundation....Pages 225-248 A Hyperelastic Dynamic Frictional Contact Model with Energy-Consistent Properties....Pages 249-275 A Non-clamped Frictional Contact Problem with Normal Compliance....Pages 277-298 On Large Time Asymptotics for Two Classes of Contact Problems....Pages 299-332 Hemivariational Inequalities for Dynamic Elastic-Viscoplastic Contact Problems....Pages 333-353 Two History-Dependent Contact Problems....Pages 355-380 Back Matter....Pages 381-383