ABSTRACT
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book
TABLE OF CONTENTS
chapter |13 pages
Blow-up rescaled equation as a gradient system: toward the generic blow-up behavior for parabolic PDEs
Variational setting and compactly supported solutions
chapter 1|5 pages
11 Problem “fast diffusion”: L–S and other patterns
Oscillatory ODEs with analytic nonlinearities
chapter 2|2 pages
2 Countable set of p-branches of global self-similar so-lutions: general strategy
Global similarity solutions for
chapter |2 pages
Variational setting: global p-branches
Pitchfork bifurcations at local existence of global sim- ilarity profiles
chapter |18 pages
Rarefaction similarity solutions
Blow-up self-similar solutions: invariant subspace and critical blow-up “saw” exponent
chapter |5 pages
Analytic δ-deformations by the Cauchy–Kovalevskaya theo-rem
compactons for higher-order NDEs