Remarks on the Cauchy problem for the one-dimensional quadratic fractional heat equationReportar como inadecuado




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1 LMPT - Laboratoire de Mathématiques et Physique Théorique 2 Département de mathématiques Tunis

Abstract : We prove that the Cauchy problem associated with the one dimensional quadratic fractional heat equation: $u t=D x^{2\alpha} u \mp u^2,\; t\in 0,T,\; x\in \R$ or $ \T $, with $ 0-1-2 $ and ill-posed for $ s=-1-2 $. As a by-product we improve the known well-posedness results for the heat equation $\alpha=1$ by reaching the end-point Sobolev index $ s=-1 $. Finally, in the case $ 1-2



Autor: Luc Molinet - Slim Tayachi -

Fuente: https://hal.archives-ouvertes.fr/



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