Lectures on nonlinear evolution equations

摘要: 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 theorem.- 3.3 Remarks on other methods.- 4. Some inequalities.- 5. Local quasilinear hyperbolic.- 6. High energy 7. Weighted a priori 8. proofs.- 8.1 Proof of Theorem 1.1.- 8.2 ot 1.2.- 9. Other 10. Development singularities.- 11. More evolutions equations.- 11.1 Equations elasiticity.- 11.1.1 Initially isotropic media in R^3.- 11.1.2 cubic 11.2 Heat 11.3 thermoelasticity.- 11.4 Schrodinger 11.5 Klein-Gordon 11.6 Maxwell 11.7 Plate 12. Further aspects and questions.- 13. Evolution waveguides.- 13.1 Nonlinear 13.1.1 part.- 13.1.2 13.2. 13.3. elasticity 13.4 General Appendix.- A. Interpolation.- B. The Cauchy-Kowalevsky.- C. local theorem hyperbolic-parabolic systems References Notation Index.