Optimal growth rates for a viscous Hamilton-Jacobi equation

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• 作者：Philippe Lauren?ot and Philippe Souplet
• 关键词：Temporal growth rates ; viscous Hamilton ; Jacobi equation ; unilateral Laplacian estimate
• 刊名：Journal of Evolution Equations
• 出版年：2005
• 出版时间：March 2005
• 年：2005
• 卷：5
• 期：1
• 页码：123-135
• 全文大小：130 KB

文摘

The growth of the Lm-norm, m t ? t-N/m||u(t)||mt\,\mapsto\,t^{-N/m}||u(t)||m is shown to be bounded from above and from below by positive real numbers. This result indicates an asymptotic behaviour dominated by the hyperbolic Hamilton-Jacobi term of the equation. A one-sided estimate for ln u is also established.