A NOTE ON GRADIENT BLOWUP RATE OF THE INHOMOGENEOUS HAMILTON-JACOBI EQUATIONS

被引：17

作者：

Zhang, Zhengce ^{[1
]}

Li, Zhenjie ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 03期

关键词：

Gradient blowup; Hamilton-Jacobi equation; inhomogeneous; HEAT-EQUATION;

D O I：

10.1016/S0252-9602(13)60029-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The gradient blowup of the equation ut = Delta u + a(x)vertical bar del u vertical bar(P) + h(x), where p > 2, is studied. It is shown that the gradient blowup rate will never match that of the self-similar variables. The exact blowup rate for radial solutions is established under the assumptions on the initial data so that the solution is monotonically increasing in time.

引用

页码：678 / 686

页数：9

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