On the Cauchy problem for a generalized nonlinear heat equation

On the Cauchy problem for a generalized nonlinear heat equation AbstractThe paper is concerned with the Cauchy problem for a nonlinear generalized heat equation which is related to the generalized Gauss–Weierstrass semigroup via Duhamel’s principle. For the initial data we assume that they belong to some fractional Sobolev spaces. We study the existence and uniqueness of mild and strong solutions which are local in time. Moreover, they are smooth functions and belong to Lebesgue spaces with respect to the space variable. We use both fixed point arguments and mapping properties of the generalized Gauss–Weierstrass semigroup. Finally, we study the well-posedness of the problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On the Cauchy problem for a generalized nonlinear heat equation

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Publisher
De Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
D.O.I.
10.1515/gmj-2018-0020
Publisher site
See Article on Publisher Site

Abstract

AbstractThe paper is concerned with the Cauchy problem for a nonlinear generalized heat equation which is related to the generalized Gauss–Weierstrass semigroup via Duhamel’s principle. For the initial data we assume that they belong to some fractional Sobolev spaces. We study the existence and uniqueness of mild and strong solutions which are local in time. Moreover, they are smooth functions and belong to Lebesgue spaces with respect to the space variable. We use both fixed point arguments and mapping properties of the generalized Gauss–Weierstrass semigroup. Finally, we study the well-posedness of the problem.

Journal

Georgian Mathematical Journalde Gruyter

Published: Jun 1, 2018

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