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Blow-up Theories for Semilinear Parabolic Equations

  • Book
  • © 2011

Overview

Authors:
  1. Bei Hu

    1. Dept. of Applied and Computational, Mathematics and Statistics, University of Notre Dame, Notre Dame, USA

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  • 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.

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2018)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Bei Hu
    Pages 1-5

  3. A Review of Elliptic Theories

    • Bei Hu
    Pages 7-18

  4. A Review of Parabolic Theories

    • Bei Hu
    Pages 19-27

  5. A Review of Fixed Point Theorems

    • Bei Hu
    Pages 29-31

  6. Finite Time Blow-Up for Evolution Equations

    • Bei Hu
    Pages 33-46

  7. Steady-State Solutions

    • Bei Hu
    Pages 47-63

  8. Blow-Up Rate

    • Bei Hu
    Pages 65-83

  9. Asymptotically Self-Similar Blow-Up Solutions

    • Bei Hu
    Pages 85-95

  10. One Space Variable Case

    • Bei Hu
    Pages 97-118

  11. Back Matter

    Pages 127-127
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Dept. of Applied and Computational, Mathematics and Statistics, University of Notre Dame, Notre Dame, USA

    Bei Hu

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