Remarks on the Cauchy problem for the one-dimensional quadratic fractional heat equationReport as inadecuate




Remarks on the Cauchy problem for the one-dimensional quadratic fractional heat equation - Download this document for free, or read online. Document in PDF available to download.

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



Author: Luc Molinet - Slim Tayachi -

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



DOWNLOAD PDF




Related documents