Differential and Integral Equations

The initial-boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity

Paolo Secchi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study the asymptotic blow-up behavior of nonnegative solutions to the quasilinear heat equation $$ u_t = (u^2)_{xx} + u^2 \quad \text{for $x \in \mathbf{R}, \,\, t > 0$}, $$ with nonnegative, bounded, continuous initial data. We give a complete classification of all possible types of blow-up behavior for compactly supported initial data. For data which look like a step function we construct self-similar blow-up patterns (logarithmic traveling wave solutions) for which the corresponding blow-up sets are empty.

Article information

Source
Differential Integral Equations, Volume 9, Number 4 (1996), 671-700.

Dates
First available in Project Euclid: 7 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367969881

Mathematical Reviews number (MathSciNet)
MR1401431

Zentralblatt MATH identifier
0853.35067

Subjects
Primary: 35L50: Initial-boundary value problems for first-order hyperbolic systems

Citation

Secchi, Paolo. The initial-boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. Differential Integral Equations 9 (1996), no. 4, 671--700. https://projecteuclid.org/euclid.die/1367969881


Export citation