Blow-up Theories for Semilinear Parabolic Equations

by Bei Hu

Overview

There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Product Details

ISBN-13:	9783642184598
Publisher:	Springer Berlin Heidelberg
Publication date:	04/06/2011
Series:	Lecture Notes in Mathematics , #2018
Edition description:	2011
Pages:	127
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

1 Introduction.- 2 A review of elliptic theories.- 3 A review of parabolic theories.- 4 A review of fixed point theorems.-5 Finite time Blow-up for evolution equations.- 6 Steady-State solutions.- 7 Blow-up rate.- 8 Asymptotically self-similar blow-up solutions.- 9 One space variable case

Editorial Reviews

From the reviews:

“The book approaches the blow-up theories for semilinear parabolic equations using maximum principles and a priori estimates. … this book is an excellent mathematical monograph and a valuable reference for researchers in the field of nonlinear partial differential equations. This book also clearly benefits instructors who need a solid and updated text for a topic course in partial differential equations. The author has produced a commendable work of scholarly achievement.” (Hongwei Chen, Mathematical Reviews, Issue 2012 i)

“These lecture notes are intended for graduate students … of basic theory of second-order parabolic and elliptic equations. … At the end of each chapter, there is a set of well-chosen exercises. … It is a nice addition to the existing literature on blow-up since the previous books were mostly intended for more advanced readers.” (Marek Fila, Zentralblatt MATH, Vol. 1226, 2012)

From the Publisher