Reinhard Racke

Lectures on Nonlinear Evolution Equations (eBook, PDF)

Initial Value Problem

• Format: PDF

Produktbeschreibung

This book serves as an elementary, self contained introduction into some important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The presentation is made using the classical method of continuation of local solutions with the help of a priori estimates obtained for small data.

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Produktdetails

• Verlag: Vieweg+Teubner Verlag
• Seitenzahl: 260
• Erscheinungstermin: 29. Juni 2013
• Englisch
• ISBN-13: 9783663106296
• Artikelnr.: 53088976

Autorenporträt

Dr. Reinhard Racke, Institut für Angewandte Mathematik,Universität Bonn/ Prof. Dr. Klas Diederich, Mathematisches Institut der Universität Wuppertal.

Inhaltsangabe

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.- B. The Theorem of Cauchy-Kowalevsky.- C. A local existence theorem for hyperbolic-parabolic systems References Notation Index.