内容提要 《阻尼波动方程解的整体存在性和衰减估计（英文版）》内容涉及正则性赢得型和正则性损失型两类耗散波动方程的渐近性态。其一是广义双色散方程等正则性赢得型耗散波动方程的整体存在性、衰减估计、渐近性态、逐点衰减估计及加权衰减估计等等。通过对解算子的详尽分析，建立由波动方程、热方程的基本解以及非线性项表示的渐近性态。其二是结构耗散的广义双色散方程、具有阻尼项六阶Boussinesq 型方程等正则性损失型耗散波动方程的整体存在性、衰减估计、渐近性态等等等。结合解算子的衰减性质，引进时间加权的能量克服正则性损失型造成的衰减性质差的困难，进而证明整体解的存在性和渐近性态。 目录 Contents Preface Chapter 1 Preliminary 1 1.1 Lp space 1 1.2 Sobolev spaces 2 1.3 Abstract functions valued iBanach spaces 4 1.4 Fourier transform 5 1.4.1 Fourier transform of L1 space 5 1.4.2 Fourier transform of Schwartz functiospace 6 1.4.3 Fourier transform of Lp(1≤p≤2) space 7 1.5 Decay rate of solutions to the initial value problem for linear heat equatio9 1.6 Calculus of inequalities 10 1.7 Some useful inequalities 11 Chapter 2 Asymptotic Profile of Solutions to the Double DispersioEquatio13 2.1 Introductio13 2.2 Analysis of Solutiooperators 16 2.3 Decay estimate of solutions to (2.2.1)， (2.1.2) 21 2.4 Asymptotic profile of solutions to (2.2.1)， (2.1.2) 25 2.5 Applications of asymptotic profile 33 2.5.1 ApplicatioI 34 2.5.2 ApplicatioII 34 2.6 Decay estimate of solutions to (2.1.1)， (2.1.2) 35 Chapter 3 Asymptotic Profile of Solutions to the Linearized Double DispersioEquatioothe Half Space Rn+ 39 3.1 Introductio39 3.2 Solutiooperators 41 3.3 Asymptotic profile of solutions to (3.1.7)， (3.1.8) 47 3.4 Asymptotic profile of solutions to the initial boundary value problem (3.1.4)–(3.1.6) 55 Chapter 4 Asymptotic Profile of Global Solutions to the Generalized Double DispersioEquatiovia the Nonlinear Term. 57 4.1 Introductio57 4.2 Analysis of solutiooperators 59 4.3 Weighted decay estimate of solutions 64 4.4 Asymptotic profile 69 Chapter 5 Pointwise Estimate of Global Small Solutions to the Generalized Double DispersioEquatio76 5.1 Introductio76 5.2 Analysis of solutiooperators 78 5.3 Global classical solutions 81 5.4 Pointwise estimate of solutiooperators 86 5.4.1 Pointwise estimate for GL and HL 86 5.4.2 Pointwise estimate for GH and HH 91 5.4.3 Pointwise estimate of G and H 92 5.5 Pointwise estimate of global classical solutions 92 Chapter 6 Global Estence and Asymptotic Behavior of Solutions for a Semi-linear Wave Equatio95 6.1 Introductio95 6.2 Solutioformula 97 6.3 Decay property 99 6.4 Decay estimate of solutions to (6.1.3)， (6.1.2) with L1 data 105 6.5 Global estence and asymptotic behavior with L1 data 110 6.6 Decay of solutions to (6.1.3)， (6.1.2) with L2 data 121 6.7 Global estence and asymptotic behavior with L2 data 124 Chapter 7 Asymptotic Behavior of Solutions to a Class of Nonlinear Wave Equations of Sixth Order with Damping 133 7.1 Introductio133 7.2 Solutiooperators 135 7.3 Decay rate of solutions to linear problem 138 7.4 Asymptotic profile of solutions to linear problem 143 7.5 Decay estimate of solutions to nonlinear problem 152 Chapter 8 Asymptotic Profile of Solutions to the Generalized Double DispersioEquatiowith Structural Damping 157 8.1 Introductio157 8.2 Mild formulatioand solutiooperators 160 8.2.1 Mild formulatio160 8.2.2 Decay property of solutiooperators 161 8.3 Global estence and time-decay 167 8.4 Asymptotic profile 173 8.4.1 The case for ν ∈ (0， 1/2) 173 8.4.2 The case ν ∈ (1/2， 1) 180 8.4.3 The case for ν = 1/2 189 Bibliography 196 Index 203 作者介绍
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