Geometry

Download E-books Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations (Monographs and Research Notes in Mathematics) PDF

By Victor A. Galaktionov, Enzo L. Mitidieri

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

The publication first reports the actual self-similar singularity suggestions (patterns) of the equations. This process permits 4 diversified periods of nonlinear PDEs to be taken care of at the same time to set up their awesome universal positive factors. The ebook describes many houses 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 ebook demonstrates that quasilinear degenerate higher-order PDEs, even unique and awkward ones, aren't as daunting as they first look. It additionally illustrates the deep beneficial properties shared by way of different types of nonlinear PDEs and encourages readers to strengthen additional this unifying PDE strategy from different viewpoints.

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