Abstract
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.
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© 2004 Birkhäuser Boston
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Galaktionov, V.A., Vázquez, J.L. (2004). Equation ut = uxx + u ln2u: Regional Blow-up. In: A Stability Technique for Evolution Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 56. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2050-3_9
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DOI: https://doi.org/10.1007/978-1-4612-2050-3_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7396-7
Online ISBN: 978-1-4612-2050-3
eBook Packages: Springer Book Archive