By Victor A. Galaktionov
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations indicates how 4 forms of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities via their targeted quasilinear degenerate representations. The authors current a unified method of care for those quasilinear PDEs.
The e-book first reviews the actual self-similar singularity recommendations (patterns) of the equations. This process permits 4 diversified periods of nonlinear PDEs to be handled at the same time to set up their outstanding universal positive aspects. The e-book describes many homes of the equations and examines conventional questions of existence/nonexistence, uniqueness/nonuniqueness, worldwide asymptotics, regularizations, shock-wave concept, 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, should not as daunting as they first look. It additionally illustrates the deep positive aspects shared via various kinds of nonlinear PDEs and encourages readers to strengthen extra this unifying PDE strategy from different viewpoints.