Blow-up Theories for Semilinear Parabolic Equations

• Main Author: Hu, Bei (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes in Mathematics, 2018
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Partial Differential Equations.; Applications of Mathematics.; Analysis.

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 me...

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.