具有限传播的热传导方程的经典解(英文)

CLASSICAL SOLUTIONS TO HEAT CONDUCTION WITH FINITE OF PROPAGATION GUIDED BY SECOND SOUND

研究具有限传播的热传导方程 .在一定假设下 ,得到了经典解的整体存在性及奇性的产生 .作者的结果阐明了推迟时间τ和解的光滑性的关系 :当推迟时间τ >0适当小时 ,整体光滑解存在 ;但推迟时间充分大时 。

The authors present heat conduction with finite of propagation guided by second sound.Under certain hypotheses,the global existence and the formation of singularities for classical solution are obtained.The results show that the relationship between the delay time and the smoothness of classical solutions:for small delay time τ>0,the C 1 solution globally exists,but for large τ,the Cattaneo law will fail.