Lectures on Nonlinear Evolution Equations: Initial Value Problem

by Reinhard Racke

1 Global solutions to wave equations - existence theorems.- 2 Lp-Lq-decay estimates for the linear wave equation.- 3 Linear symmetric hyperbolic systems.- 4 Some inequalities.- 5 Local existence for quasilinear symmetric hyperbolic systems.- 6 High energy estimates.- 7 Weighted a priori estimates for small data.- 8 Global solutions to wave equations - proofs.- 9 Other methods.- 10 Development of singularities.- 11 More evolution equations.- 12 Further aspects and questions.- A Interpolation.- B The Theorem of Cauchy-Kowalevsky.- C A local existence theorem for hyperbolic-parabolic systems.- References.- Notation.

272 pages, Paperback

Published March 12, 2014