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Search: All articles in the CJM digital archive with keyword heat equation

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1. CJM Online first

Saanouni, Tarek
 Global and non global solutions for some fractional heat equations with pure power nonlinearity The initial value problem for a semi-linear fractional heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method. Keywords:nonlinear fractional heat equation, global Existence, decay, blow-upCategory:35Q55

2. CJM 1999 (vol 51 pp. 673)

Barlow, Martin T.; Bass, Richard F.
 Brownian Motion and Harmonic Analysis on Sierpinski Carpets We consider a class of fractal subsets of $\R^d$ formed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusion $X$ and determine its basic properties; and extend some classical Sobolev and Poincar\'e inequalities to this setting. Keywords:Sierpinski carpet, fractal, Hausdorff dimension, spectral dimension, Brownian motion, heat equation, harmonic functions, potentials, reflecting Brownian motion, coupling, Harnack inequality, transition densities, fundamental solutionsCategories:60J60, 60B05, 60J35
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