A note on semilinear heat equation in hyperbolic space

作者：Wang, Zhiyong; Yin, Jingxue^*

来源：Journal of Differential Equations, 2014, 256(3): 1151-1156.

DOI：10.1016/j.jde.2013.10.011

• Semilinear heat equations
• Hyperbolic space
• Blow-up
• Fujita exponent

Handle et al. [1] obtained a quite interesting result about a semilinear heat equation that the Fujita exponent relative to the whole hyperbolic space is just the same as that relative to bounded domain in Euclidean space, and, in addition, the properties of solutions are different in the critical exponent case. Our purpose is to answer an open problem proposed by Bandle et al. for the critical exponent case, and it, together with the one obtained by them, shows that the critical exponent case does belong to the non-blow-up case, which is completely different from the case in Euclidean space.

• 出版日期2014-2-1
• 单位华南师范大学