A Remark on the Energy Blow-up Behavior for Nonlinear Heat Equations
نویسنده
چکیده
lim t→T ‖u(t)‖H 1 0 ( ) =+∞. A point a ∈ is called a blow-up point of u if there exists (an, tn) → (a,T ) such that |u(an, tn)| → +∞. The set of all blow-up points of u(t) is called the blow-up set and denoted by S. From Giga and Kohn [8, Theorem 5.3], there are no blow-up points in ∂ . Therefore, we see from (3) and the boundedness of that S is not empty. Many papers are concerned with the Cauchy problem for (1) (see, for instance, [21]) or the problem of finding sufficient blow-up conditions on the initial data (see
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