By Juan Luis Vázquez
Concentrating on a category of equations with nonlinearities of energy kind that result in degenerate or singular parabolicity ("equations of porous medium type"), the purpose of this article is to acquire sharp a priori estimates and rot premiums for basic periods of options when it comes to estimates of specific difficulties. those estimates are the development blocks in realizing the qualitative idea, and the decay premiums pave the right way to the high quality research of asymptotics. Many technically suitable questions are provided and analyzed intimately. a scientific photograph of the main suitable phenomena is acquired for the equations lower than learn, together with time decay, smoothing, extinction in finite time, and not on time regularity.
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Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type (Oxford Lecture Series in Mathematics and Its Applications) by Juan Luis Vázquez