Abstract
We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local Lr spaces. Furthermore, we study the sharp lower estimates of the blow-up time of the solutions with the initial data λψ as λ → 0 or λ → ∞ and the lower blow-up estimates of the solutions.
Original language | English |
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Pages (from-to) | 2627-2652 |
Number of pages | 26 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 36 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2016 May |
Keywords
- Blow-up rate
- Blow-up time
- Heat equation
- Nonlinear boundary condition
- Uniformly local L spaces
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics