Blowup in Nonliear Heat Equations

Doctoral Dissertation

Abstract

We study the blowup problem for nonlinear heat equations. We show that if the even initial value is close enough to a 2-dimensional manifold of approximately homogenous solutions, the solution blows up in a finite time and the asymptotical profile is an approximate solution with parameters evolving according to a certain dynamical system plus a small fluctuation in $L^infty$.

The result allows us to construct initial data with more than one local maximum while the solutions still blow up in a finite time according to the asymptotical profile. We also demonstrated that there is an open subset in the space of initial data and their solutions blow up according to the described asymptotical profile.

Attributes

Attribute NameValues
URN
  • etd-12082006-212708

Author Shuangcai Wang
Advisor Grant J. Mathews
Contributor Mark S. Alber, Committee Member
Contributor Bei Hu, Committee Member
Contributor Gerard K. Misiolek, Committee Member
Contributor Grant J. Mathews, Committee Chair
Contributor Israel Michael Sigal, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2006-09-08

Submission Date 2006-12-08
Country
  • United States of America

Subject
  • partial differential equations

  • blowup

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

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