By Victor A. Galaktionov
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations indicates how 4 different types 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 booklet first stories the actual self-similar singularity options (patterns) of the equations. This technique permits 4 diverse periods of nonlinear PDEs to be handled at the same time to set up their awesome universal positive aspects. The e-book describes many houses of the equations and examines conventional questions of existence/nonexistence, uniqueness/nonuniqueness, worldwide asymptotics, regularizations, shock-wave thought, and diverse blow-up singularities.
Preparing readers for extra complex mathematical PDE research, the ebook demonstrates that quasilinear degenerate higher-order PDEs, even unique and awkward ones, usually are not as daunting as they first look. It additionally illustrates the deep positive aspects shared through various kinds of nonlinear PDEs and encourages readers to improve extra this unifying PDE strategy from different viewpoints.