A Tracing of the Fractional Temperature Field

Abstract

This note is devoted to a study of $L^q$-tracing of the fractional temperature field $u(t,x)$ -- the weak solution of the fractional heat equation $({\partial }_t+(-{\Delta }_x{)}^{\alpha })u(t,x)=g(t,x)$ in $L^p({\mathbb{R}}_{+}^{1+n})$ subject to the initial temperature $u(0,x)=f(x)$ in $L^p({\mathbb{R}}^n)$.

20 pages

References in corpus (2)

• Well-posedness of the Cauchy problem for the fractional power dissipative equations
• Heat kernel estimates for critical fractional diffusion operator