Blow-up Theories for Semilinear Parabolic Equations

There is a range of literature dealing with the blow-up behavior of evolution equations, but this book's fresh approach elucidates the theory by focusing on methodology, eschewing large-scale technical computations in favor of a simple illustrative equation.

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.

There are many lengthy books in blowup theories, this one is short and appropriate for graduate students. Emphasize the methods, avoid massive technical computations. Good enough for a one semester course.

Inhalt
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