This book introduces a new, state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations; much of the text is dedicated to the application of this method to a wide class of nonlinear diffusion equations. The underlying theory hinges on a new stability result, formulated in the abstract setting of infinite-dimensional dynamical systems, which states that under certain hypotheses, the omega-limit set of a perturbed dynamical system is stable under arbitrary asymptotically small perturbations.The Stability Theorem is examined in detail in the first chapter, followed by a review of basic results and methods---many original to the authors---for the solution of nonlinear diffusion equations. Further chapters provide a self-contained analysis of specific equations, with carefully-constructed theorems, proofs, and references. In addition to the derivation of interesting limiting behaviors, the book features a variety of estimation techniques for solutions of semi- and quasilinear parabolic equations.Written by established mathematicians at the forefront of the field, this work is a blend of delicate analysis and broad application... 7.23 Let N = 2, c agt; 21/mC* and uq(x) s 0. There are values 0 alt; s alt; 1/2, T Ar 1 and 0 alt; a alt; Vl - 2e such that the rescaled solution w of problem (7.1) satisfies ... 02 2 V ^ yT2) WrX(ln(|||0))Ja#39; where v a (m a l)/m. The first term in square brackets, anbsp;...
|Title||:||A Stability Technique for Evolution Partial Differential Equations|
|Author||:||Victor A. Galaktionov, Juan Luis Vázquez|
|Publisher||:||Springer Science & Business Media - 2004|