Download Blow-up for higher-order parabolic, hyperbolic, dispersion by Victor A. Galaktionov PDF

By Victor A. Galaktionov

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations indicates how 4 kinds of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities via their specific quasilinear degenerate representations. The authors current a unified method of care for those quasilinear PDEs.

The publication first reviews the actual self-similar singularity strategies (patterns) of the equations. This process permits 4 diversified sessions of nonlinear PDEs to be handled concurrently to set up their impressive universal beneficial properties. The booklet describes many homes of the equations and examines conventional questions of existence/nonexistence, uniqueness/nonuniqueness, worldwide asymptotics, regularizations, shock-wave conception, and numerous blow-up singularities.

Preparing readers for extra complicated mathematical PDE research, the booklet demonstrates that quasilinear degenerate higher-order PDEs, even unique and awkward ones, should not as daunting as they first look. It additionally illustrates the deep gains shared by means of various kinds of nonlinear PDEs and encourages readers to improve additional this unifying PDE strategy from different viewpoints.

Show description

Read or Download Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations PDF

Similar geometry books

A Survey of Geometry (Revised Edition)

From the book's preface:
Since writing the preface of the 1st version of this paintings, the gloomy plight there defined of starting collegiate geometry has brightened significantly. The pendulum turns out certainly to be swinging again and a goodly quantity of good textual fabric is showing.

How to Solve Word Problems in Geometry (How to Solve Word Problems)

One of the best ways to resolve the toughest difficulties! Geometry's wide use of figures and visible calculations make its be aware difficulties specifically tough to resolve. This booklet choices up the place so much textbooks go away off, making suggestions for fixing difficulties effortless to know and providing many illustrative examples to make studying effortless.

Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations exhibits how 4 varieties of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities via their distinct quasilinear degenerate representations. The authors current a unified method of care for those quasilinear PDEs.

Differential Geometry of Submanifolds and Its Related Topics

This quantity is a compilation of papers awarded on the convention on differential geometry, particularly, minimum surfaces, actual hypersurfaces of a non-flat complicated area shape, submanifolds of symmetric areas and curve idea. It additionally includes new effects or short surveys in those components. This quantity presents basic wisdom to readers (such as differential geometers) who're attracted to the idea of actual hypersurfaces in a non-flat advanced area shape.

Additional info for Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrödinger equations

Example text

Periodic solutions, together with their stable manifolds, are simple connections with the interface, as a singular point of ODE (9). Note that (102) does not admit variational setting, so we cannot apply well-developed potential theory [303, Ch. 8] (see a large amount of related existence–nonexistence results and further references therein), or a degree one 1 Self-Similar Blow-up and Compacton Patterns 31 [251, 252]. 1], which can be extended to m = 3 as well. Nevertheless, uniqueness of a periodic orbit is still open, so we conjecture the following result supported by various numerical and analytical evidence (cf.

9269... H(v Genus three. Similarly, for k = 3 (genus ρ = 3), there are several patterns that seem to deliver the L–S critical value c3 . 3. 0710... is given by the basic F2 . 1; m = 2 and n = 1. 2; m = 2 and n = 1. 2 are very close to each other. 31607... 6203... 1324... H(v Note that the S–L category-genus construction (74) itself guarantees that all solutions {vk } as critical points will be (geometrically) distinct; see [252, p. 381]. Here we stress two important conclusions: (I) First, what is key for us is that closed subsets in H0 of functions of the sum type in (88) do not deliver S–L critical values in (74).

L–S theory and direct application of fibering method The functional (64) is C 1 , uniformly differentiable, and weakly continuous, so we can apply the classic Lusternik–Schnirel’man (L–S) theory of calculus of variations [252, § 57] in the form of the Pohozaev’s fibering method [327, 329], as a convenient generalization of previous versions [77, 340] of variational approaches. Namely, following L–S and Pohozaev’s fibering theory [329], the number of critical points of the functional (64) depends on the category (or genus) of the functional subset, on which fibering is taking place.

Download PDF sample

Rated 4.41 of 5 – based on 47 votes