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

Luc Molinet, Slim Tayachi

We prove that the Cauchy problem associated with the one dimensional quadratic (fractional) heat equation: $u_t=D_x^{2\alpha }u\mp u^2,t\in (0,T),x\in \mathbb{R}$ or $ \T $, with $ 0<α\l…