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Zeitschrift für Analysis und ihre Anwendungen


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Volume 38, Issue 3, 2019, pp. 287–308
DOI: 10.4171/ZAA/1638

Published online: 2019-07-15

On the Existence and Uniqueness of Mild and Strong Solutions of a Generalized Nonlinear Heat Equation

Franka Baaske[1] and Hans-Jürgen Schmeisser[2]

(1) Friedrich-Schiller-Universität Jena, Germany
(2) Friedrich-Schiller-Universität Jena, Germany

In this paper, we study well-posedness of the Cauchy problem for a nonlinear generalized heat equation with initial data in Besov and Triebel{Lizorkin spaces. We prove existence and uniqueness of mild and strong solutions which are local in time. The crucial point is the use of estimates and mapping properties of the generalized Gauss{Weierstrass semigroup in function spaces under consideration. Moreover, we study regularity properties of solutions with respect to space and time.

Keywords: Nonlinear generalized heat equation, mild and strong solutions, supercritical function spaces of Besov and Triebel{Lizorkin type, well-posedness

Baaske Franka, Schmeisser Hans-Jürgen: On the Existence and Uniqueness of Mild and Strong Solutions of a Generalized Nonlinear Heat Equation. Z. Anal. Anwend. 38 (2019), 287-308. doi: 10.4171/ZAA/1638