EDP Sciences 1775437021 20260406 fre

laboutique.edpsciences.fr-R002837 03 01 01 R002837 00 ED E107 00 01 01 Global Existence and Decay Estimate of Solutions to Damped Wave Equations 01 eng 08 214 03 22 2382425 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 11 00 20260324 02 01 003006 03 9782759839896 15 9782759839896 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-003006 03 01 01 003006 03 9782759839896 15 9782759839896 10 EA E107 10 00 01 R002837 ED E107 1 10 01 02 Current Natural Sciences 01 01 Global Existence and Decay Estimate of Solutions to Damped Wave Equations 1 A01 01 A2442 Yuzhu WANG WANG, Yuzhu Yuzhu WANG Yuzhu WANG is Professor of Mathematics at the School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, China. He received his Ph.D. in Applied Mathematics from Shanghai Jiao Tong University. His research focuses on nonlinear partial differential equations. 01 eng 08 212 03 01 20 Damped wave equations;double dispersion equations;abstract analysis;applied analysis;dissipative hyperbolic equations 10 2011 MAT007020 29 CLIL3054 01 510 05 03 00 This book presents recent advances on the global existence and decay estimates of solutions to two important classes of damped wave equations, with particular emphasis on the double dispersion equation and related models. Building on the author’s work with collaborators, the volume brings together results previously scattered across research papers, alongside new material published here for the first time. It offers a unified perspective on the long-standing problem of global existence and the asymptotic behavior of dissipative hyperbolic equations, including convergence toward equilibrium and optimal decay properties.The book is organized into eight chapters. The opening chapter reviews essential tools from Fourier analysis, Sobolev spaces, and fundamental inequalities. Subsequent chapters investigate the asymptotic profiles, decay rates, and pointwise behavior of solutions to regularity-gained double dispersion equations, followed by a systematic study of regularity-loss wave equations. Techniques such as time-weighted energy methods and refined asymptotic analysis are developed to address weak dissipation and nonlinear effects, establishing global existence and precise decay estimates under suitable initial conditions and spatial dimensions.Combining rigorous theory with clear structure, this book highlights both foundational methods and recent progress in nonlinear partial differential equations. It is intended for graduate students, researchers, and specialists interested in nonlinear wave phenomena, dissipative systems, and modern analytical techniques in PDEs. This bookpresents recent advances on the global existence and decay estimates ofsolutions to two important classes of damped wave equations, with particularemphasis on the double dispersion equation and related models. Building on theauthor’s work with collaborators, the volume brings together results previouslyscattered across research papers, alongside new material published here for thefirst time. It offers a unified perspective on the long-standing problem ofglobal existence and the asymptotic behavior of dissipative hyperbolicequations, including convergence toward equilibrium and optimal decayproperties.<o:p></o:p>The book isorganized into eight chapters. The opening chapter reviews essential tools fromFourier analysis, Sobolev spaces, and fundamental inequalities. Subsequentchapters investigate the asymptotic profiles, decay rates, and pointwisebehavior of solutions to regularity-gained double dispersion equations, followedby a systematic study of regularity-loss wave equations. Techniques such astime-weighted energy methods and refined asymptotic analysis are developed toaddress weak dissipation and nonlinear effects, establishing global existenceand precise decay estimates under suitable initial conditions and spatialdimensions.<o:p></o:p>Combiningrigorous theory with clear structure, this book highlights both foundationalmethods and recent progress in nonlinear partial differential equations. It isintended for graduate students, researchers, and specialists interested innonlinear wave phenomena, dissipative systems, and modern analytical techniquesin PDEs.<o:p></o:p> 02 00 This book presents recent advances on the global existence and decay estimates of solutions to two important classes of damped wave equations, with particular emphasis on the double dispersion equation and related models. 04 00 See 'Complements' 21 00 06 01 https://laboutique.edpsciences.fr/produit/1558/9782759839896/global-existence-and-decay-estimate-of-solutions-to-damped-wave-equations 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/983/578/original/9782759839889-Global_Existence_and_Decay_Estimate_of_Solutions_to_Damped_Wave_Equations_couv-sofedis.jpg 17 14 20260312T155826+0100 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20260324 01 00 20260324 19 00 20260324 2026 06 3052868830012 01 WORLD 13 03 9782759839889 15 9782759839889 WORLD 08 EDP Sciences & Science Press 04 01 00 20260324 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 52.99 01 5.50 2.76 EUR 04 06 01 02 1 00 187.99 01 5.50 2.76 EUR 01 04 06 01 02 1 00 206.99 01 5.50 10.79 USD 01