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

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 pages

F(y)

chapter |16 pages

Basic computations

chapter |2 pages

The second energy relation

chapter |1 pages

A diversion to blow-up for n > 0

chapter 1|5 pages

11 Problem “fast diffusion”: L–S and other patterns

Oscillatory ODEs with analytic nonlinearities

chapter |3 pages

||F||

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 |20 pages

Simple eigenvalues

chapter |13 pages

f(y)

chapter |3 pages

The blow-up results

chapter 4|19 pages

6 Single-point blow-up for p > n+1

chapter |2 pages

center subspace behavior for k = 2

chapter 7|5 pages

3 Proofs of blow-up results

chapter |2 pages

Self-focusing (cumulation) phenomenon

chapter |7 pages

NDE–3 is not a hyperbolic system

chapter |18 pages

Rarefaction similarity solutions

Blow-up self-similar solutions: invariant subspace and critical blow-up “saw” exponent

chapter 8|24 pages

14 Gradient blow-up similarity solutions

chapter 8|10 pages

17 Fifth-order NDEs and main problems

chapter |13 pages

Existence of a shock similarity profile

chapter |9 pages

f(y)

chapter |4 pages

F(y)

chapter |5 pages

Analytic δ-deformations by the Cauchy–Kovalevskaya theo-rem

compactons for higher-order NDEs

chapter |3 pages

A formal resolvent

chapter 9|1 pages

5 Application I: evolution completeness ofΦ inL(IR

Linear PDEs

chapter |11 pages

NLSE: on a “center subspace” behavior

chapter |8 pages

First kernel scaling

chapter |2 pages

Little Hilbert and Sobolev spaces

chapter |21 pages

References

chapter |1 pages

List of Frequently Used Abbreviations