Differential and Integral Equations

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

Paolo Secchi

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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


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