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	Jump processes and nonlinear fractional heat equations on metric measure spaces
	Hu, JX ; Zahle, M
	2010-05-06 ; 2010-05-06
关键词	jump process heat kernel Dirichlet form Sobolev-Slobodeckij space fractional heat equation Hausdorff dimension walk dimension BROWNIAN-MOTION D-SETS FRACTALS Mathematics
中文摘要	Jump processes on metric-measure spaces are investigated by using heat kernels. It is shown that the heat kernel corresponding to a sigma-stable type process decays at a polynomial rate rather than at an exponential rate as a Brownian motion. The domain of the Dirichlet form associated with the jump process is a Sobolev-Slobodeckij space, and the embedding theorems for this space are derived by using the heat kernel technique. As an application, we investigate nonlinear fractional heat equations of the form partial derivative u/partial derivative t(t,x) = -(-Delta)(sigma) u(t,x) + u(t,x)(p) non-negative initial values on a metric-measure space F, and show the non-existence of non-negative global solution if 1 < p <= 1 + sigma beta/alpha, where alpha is the Hausdorff dimension of F whilst beta is the walk dimension of F. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
语种	英语 ; 英语
出版者	WILEY-V C H VERLAG GMBH ; WEINHEIM ; PO BOX 10 11 61, D-69451 WEINHEIM, GERMANY
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14296]
专题	清华大学
推荐引用方式 GB/T 7714	Hu, JX,Zahle, M. Jump processes and nonlinear fractional heat equations on metric measure spaces[J],2010, 2010.
APA	Hu, JX,&Zahle, M.(2010).Jump processes and nonlinear fractional heat equations on metric measure spaces..
MLA	Hu, JX,et al."Jump processes and nonlinear fractional heat equations on metric measure spaces".(2010).

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