Acta mathematica scientia, Series B >
A NOTE ON GRADIENT BLOWUP RATE OF THE INHOMOGENEOUS HAMILTON-JACOBI EQUATIONS
Received date: 2011-06-16
Revised date: 2011-09-11
Online published: 2013-05-20
Supported by
The first author is supported by Youth Foundation of NSFC (10701061), Fundamental Research Funds for the Central Universities of China, and Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
The gradient blowup of the equation ut = Δu + a(x)|∇u|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.
Key words： Gradient blowup; Hamilton-Jacobi equation; inhomogeneous
ZHANG Zheng-Ce , LI Zhen-Jie . A NOTE ON GRADIENT BLOWUP RATE OF THE INHOMOGENEOUS HAMILTON-JACOBI EQUATIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 678 -686 . DOI: 10.1016/S0252-9602(13)60029-6
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