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.
Citation
Paolo Secchi. "The initial-boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity." Differential Integral Equations 9 (4) 671 - 700, 1996. https://doi.org/10.57262/die/1367969881
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