ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF A SEMILINEAR HEAT EQUATION WITH LOCALIZED REACTION

作者：Suzuki Ryuichi^*

来源：Advances in Differential Equations, 2010, 15(3-4): 283-314.

We consider non-negative solutions to the Dirichlet problem of a semilinear heat equation with localized reaction in Omega: ut = Du + f (u(x(0)(t), t)), where Omega is a smooth bounded domain, x(0)(t) is a locally Holder continuous function from (0, infinity) into Omega and f satisfies f (0) = f'(0) = 0 and some blow-up condition. We show that, if x(0)(t) remains in some compact subset of S2 as t -> infinity, then all global solutions are bounded in 0 x (0, infinity) and, if x(0)(t) approaches the boundary of S2 as t -> infinity, then some unbounded global solution (infinite time blow-up solution) exists. These results are parts of our main results on the classification of all solutions.

• 出版日期2010-4