Equation ut = uxx + u ln2u: Regional Blow-up
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.
KeywordsStability Technique Strong Maximum Principle Evolution Partial Differential Equation Asymptotic Profile Quasilinear Heat Equation
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