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非线性双曲微分方程讲义PDF|Epub|txt|kindle电子书版本网盘下载
- L.HORMANDER编 著
- 出版社： 世界图书出版公司北京公司
- ISBN：7506260107
- 出版时间：2003
- 标注页数：289页
- 文件大小：84MB
- 文件页数：302页
- 主题词：
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图书目录
Chapter Ⅰ．Ordinary differential equations1
1.1．Introduction1
1.2．Local existence and uniqueness for the Cauchy problem1
1.3．Existence of solutions in the large6
1.4．Generalized solutions9
Chapter Ⅱ．Scalar first order equations with one space variable13
2.1．Introduction13
2.2．The linear case13
2.3．Classical solutions of Burgers'equation15
2.4．Weak solutions of Burgers'equation17
2.5．General strictly convex conservation laws28
Chapter Ⅲ．Scalar first order equations with several variables36
3.1．Introduction36
3.2．Parabolic equations36
3.3．The conservation law with viscosity41
3.4．The entropy solution of the conservation law41
Chapter Ⅳ．First order systems of conservation laws with one space variable46
4.1．Introduction46
4.2．Generalities on first order systems46
4.3．The lifespan of classical solutions56
4.4．The Riemann problem59
4.5．Glimm's existence theorem63
4.6．Entropy pairs70
Chapter Ⅴ．Compensated compactness72
5.1．Introduction72
5.2．Weak convergence in L∞72
5.3．Weak convergence of solutions of linear differential equations77
5.4．A scalar conservation law with one space variable80
5.5．Probability measures associated with a system of two equations83
5.6．Existence of weak solutions for a system of two equations87
Chapter Ⅵ．Nonlinear perturbations of the wave equation89
6.1．Introduction89
6.2．The linear wave equation91
6.3．The energy integral method96
6.4．Interpolation and Sobolev inequalities106
6.5．Global existence theorems for nonlinear wave equations117
6.6．The null condition in three dimensions130
6.7．Global existence theorems by the conformal method141
Chapter Ⅶ．Nonlinear perturbations of the Klein-Gordon equation145
7.1．Introduction145
7.2．Asymptotic behavior of solutions of the Klein-Gordon equation145
7.3．L2．L∞ estimates for the Klein-Gordon equation155
7.4．Existence theorems162
7.5．Remarks on the lowest space dimensions168
7 6．Alternative energy and Sobolev estimates171
7.7．Existence theorems for Cauchy data of compact support174
7.8．The method of Shatah176
Chapter Ⅷ．Microlocal analysis186
8.1．Introduction186
8.2．The wave front set186
8.3．Microlocal regularity of a product189
8.4．Pseudo-differential operators193
8.5．Composite functions200
8.6．H？lder and Zygmund classes201
Chapter Ⅸ．Pseudo-differential operators of type 1,1211
9.1．Introduction211
9.2．Some basic facts on pseudo-differential operators212
9.3．Continuity in H(s)and in C？213
9.4．Adjoints224
9.5．Composition226
9.6．Symbols with additional smoothness227
9.7．The sharp G？rding inequality233
Chapter Ⅹ．Paradifferential calculus235
10.1．Introduction235
10.2．Regularisation of symbols and paradifferential calculus235
10.3．Bony's linearisation theorem240
Chapter Ⅺ．Propagation of singularities246
11.1．Introduction246
11.2．First order scalar differential equations246
11.3．Linear pseudo-differential equations251
11.4．Nonlinear differential equations255
11.5．Second order hyperbolic equations257
11.6．Beals'restriction theorem263
Appendix on pseudo-Riemannian geometry270
A.1．Basic definitions270
A.2．Geodesic coordinates and curvature270
A.3．Conformal changes of metric275
A.4．A conformal imbedding of Minkowski space277
References283
Index of notation286
Index288