Remarks on the Cauchy problem for the one-dimensional quadratic fractional heat equation

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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

Author: Luc Molinet - Slim Tayachi -

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