Equation ut = uxx + u ln2u: Regional Blow-up

  • Victor A. Galaktionov
  • Juan Luis Vázquez
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 56)


The main goal of this chapter is to show that there exists a remarkable semilinear heat equation with regional blow-up described by an associated first-order Hamilton—Jacobi eqaution. In our asymptotic analysis, we obtain a singularly perturbed dynamical system and apply the S-Theorem adapted to the case of the stability of reduced omega-limit sets.


Stability Technique Strong Maximum Principle Evolution Partial Differential Equation Asymptotic Profile Quasilinear Heat Equation 
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Copyright information

© Birkhäuser Boston 2004

Authors and Affiliations

  • Victor A. Galaktionov
    • 1
    • 2
  • Juan Luis Vázquez
    • 3
  1. 1.Department of Mathematical SciencesUniversity of BathBathUK
  2. 2.Keldysh Institute of Applied MathematicsMoscowRussia
  3. 3.Department of MathematicsUniversidad Autónoma de MadridMadridSpain

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