Lectures on Nonlinear Evolution Equations

Initial Value Problems

Häftad, Engelska, 2016

AvReinhard Racke

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Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations.

Produktinformation

Utgivningsdatum2016-10-22
Mått155 x 235 x 18 mm
Vikt482 g
FormatHäftad
SpråkEngelska
Antal sidor306
Upplaga2
FörlagBirkhauser Verlag AG
ISBN9783319342597
OriginaltitelLectures on Nonlinear Evolution Equations. Initial Value Problem

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Beräkning och matematisk analys inom Naturvetenskap och teknik

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.