Springfield: American Institute of Mathematical Sciences
We study nonnegative radially symmetric solutions for a semilinear heat equation in a ball with spatially dependent coeﬃcient which vanishes at the origin. Our aim is to construct a solution that blows up at the origin where there is no reaction. For this, we ﬁrst prove that the blow-up is complete, if the origin is not a blow-up point and if there is no blow-up point on the boundary. Then we prove that a threshold solution exists such that it blows up in ﬁnite time incompletely and there is no blow-up point on the boundary. On the other hand, we prove that any zero of nonnegative potential is not a blow-up point for a more general problem under the assumption that the solution is monotone in time.
Communications on Pure and Applied Analysis 10(1), pp.161-177