<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we prove that the global attractor generated by strong solutions of a reaction-diffusion equation without uniqueness of the Cauchy problem is bounded in suitable <italic>Lr</italic>-spaces. In order to obtain this result we prove first that the concepts of weak and mild solutions are equivalent under an appropriate assumption.Also, when the nonlinear term of the equation satisfies a supercritical growth condition the existence of a weak attractor is established.</abstract>

In this paper we prove that the global attractor generated by strong solutions of a reaction-diffusion equation without uniqueness of the Cauchy problem is bounded in suitable Lr-spaces. In order to obtain this result we prove first that the concepts of weak and mild solutions are equivalent under an appropriate assumption.Also, when the nonlinear term of the equation satisfies a supercritical growth condition the existence of a weak attractor is established.

On <italic>Lr</italic>-regularity of global attractors generated by strong solutions of reaction-diffusion equations

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On -regularity of global attractors generated by strong solutions of reaction-diffusion equations

In this paper we prove that the global attractor generated by strong solutions of a reaction-diffusion equation without uniqueness of the Cauchy problem is...

On L^r-regularity of global attractors generated by strong solutions of reaction-diffusion equations

Published Online: Sep 16, 2016

Page range: 375 - 390

Received: Jul 28, 2016

Accepted: Sep 16, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00033

Keywords
reaction-diffusion equation, setvalued dynamical system, global attractor, multivalued semiflow

© 2016 José Valero, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Lr-regularity of global attractors generated by strong solutions of reaction-diffusion equations

Published Online: Sep 16, 2016

Page range: 375 - 390

Received: Jul 28, 2016

Accepted: Sep 16, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00033

Keywordsreaction-diffusion equation, setvalued dynamical system, global attractor, multivalued semiflow

© 2016 José Valero, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On L^r-regularity of global attractors generated by strong solutions of reaction-diffusion equations

Keywords
reaction-diffusion equation, setvalued dynamical system, global attractor, multivalued semiflow