Download e-book for iPad: Geometric Sturmian Theory of Nonlinear Parabolic Equations by Victor A. Galaktionov

in contrast to the classical Sturm theorems at the zeros of options of second-order ODEs, Sturm's evolution 0 set research for parabolic PDEs didn't allure a lot cognizance within the nineteenth century, and, in truth, it was once misplaced or forgotten for nearly a century. in brief revived through Pólya within the 1930's and rediscovered partly numerous occasions on the grounds that, it was once no longer until eventually the 1980's that the Sturmian argument for PDEs started to penetrate into the speculation of parabolic equations and was once chanced on to have a number of basic applications.

Geometric Sturmian conception of Nonlinear Parabolic Equations and functions specializes in geometric facets of the intersection comparability for nonlinear versions growing finite-time singularities. After introducing the unique Sturm 0 set effects for linear parabolic equations and the elemental thoughts of geometric research, the writer provides the most techniques and regularity result of the geometric intersection conception (G-theory). the following he considers the overall singular equation and offers the geometric notions regarding the regularity and interface propagation of options. within the basic environment, the writer describes the most features of the ODE-PDE duality, proves lifestyles and nonexistence theorems, establishes strong point and optimum Bernstein-type estimates, and derives interface equations, together with higher-order equations. the ultimate chapters discover a few targeted features of discontinuous and non-stop restrict semigroups generated through singular parabolic equations.

Much of the data provided right here hasn't ever ahead of been released in e-book shape. Readable and self-contained, this ebook kinds a different and striking reference on second-order parabolic PDEs used as versions for quite a lot of actual problems.