Lectures on nonlinear evolution equations: initial value problems
Title Statements
- Full title :Lectures on nonlinear evolution equations : initial value problems / Reinhard Racke.
Edition Statements
- Publication Date:©2015.
- Edition:Second edition
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Cham
- Language:eng
- Publication Date:©2015.
The Physical Object
- Description:1 v. (VIII-306 p.) : : illustrations, couv. illustrations ; : 24 cm
Edition Identifiers
- ISBN:9783319218724, 3319218727
- oclc:ocn965194204
- LC Classification:QA378
- Dewey Decimal:515.3/55
Table of Contents
Introduction -- 1. Global solutions to wave equations -- existence theorems -- 2. L^p -- L^q-decay estimates for the linear we equation -- 3. Linear symmetric hyperbolic systems -- 3.1 Energy estimates -- 3.2 A global existence theorem -- 3.3 Remarks on other methods -- 4. Some inequalities -- 5. Local existence for quasilinear symmetric hyperbolic -- 6. High energy estimates -- 7. Weighted a priori estimates -- 8. Global solutions to wave equations -- proofs -- 8.1 Proof of Theorem 1.1 -- 8.2 Proof ot Theorem 1.2 -- 9. Other methods -- 10. Development of singularities -- 11. More evolutions equations -- 11.1 Equations of elasiticity -- 11.1.1 Initially isotropic media in R^3 -- 11.1.2 Initially cubic media in R^3 -- 11.2 Heat equations -- 11.3 Equations of thermoelasticity -- 11.4 Schrödinger equations -- 11.5 Klein-Gordon equations -- 11.6 Maxwell equations -- 11.7 Plate equations -- 12. Further aspects and questions -- 13. Evolution equations in waveguides -- 13.1 Nonlinear wave equations -- 13.1.1 Linear part -- 13.1.2 Nonlinear part -- 13.2. Schrödinger equations -- 13.3. Equations of elasticity and Maxwell equations -- 13.4 General waveguides -- Appendix -- A. Interpolation …
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