We establish the local existence and the uniqueness of solutionsof the heat equation with a nonlinear boundary conditionfor the initial data in uniformly local Lʳ spaces.Furthermore, we study the sharp lower estimates of the blow-up timeof the solutions with the initial data λψ as λ→ 0 or λ→∞and the lower blow-up estimates of the solutions.
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Ishige et al. (2015) studied this question.
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