arXiv subjects

Franka Baaske

Publications and source records attributed to Franka Baaske.

2 recordsLinked to original sources

arXiv2024

Fractional nonlinear heat equations and characterizations of some function spaces in terms of fractional Gauss-Weierstrass semi-groups

We present a new proof of the caloric smoothing related to the fractional Gauss-Weierstrass semi-group in Triebel-Lizorkin spaces. This property will be used to prove existence and uniqueness of mild and strong solutions of the Cauchy problem for a fractional nonlinear heat equation.

math.AP↗

arXiv2023

On the Cauchy problem for a semi-linear hyperdissipative heat equation

The paper is concerned with the Cauchy problem for a semi-linear hyperdissipative heat equation in Besov and Triebel-Lizorkin spaces which is related to the generalized Gauss-Weierstrass semi-group via Duhamel's principle. Using caloric smoothing properties of the semi-group we prove existence and uniqueness of mild and strong solutions which are local in time. Moreover, we study well-posedness of the problem.

math.AP↗