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2018 Uniform stability for fractional Cauchy problems and applications
Luciano Abadias, Edgardo Álvarez
Topol. Methods Nonlinear Anal. 52(2): 707-728 (2018). DOI: 10.12775/TMNA.2018.038

Abstract

In this paper we give uniform stable spatial bounds for the resolvent operator families of the abstract fractional Cauchy problem on $\mathbb{R}_+$. Such bounds allow to prove existence and uniqueness of $\mu$-pseudo almost automorphic $\epsilon$-mild regular solutions to the nonlinear fractional Cauchy problem in the whole real line. Finally, we apply our main results to the fractional heat equation with critical nonlinearities.

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Luciano Abadias. Edgardo Álvarez. "Uniform stability for fractional Cauchy problems and applications." Topol. Methods Nonlinear Anal. 52 (2) 707 - 728, 2018. https://doi.org/10.12775/TMNA.2018.038

Information

Published: 2018
First available in Project Euclid: 25 November 2018

zbMATH: 07051688
MathSciNet: MR3915659
Digital Object Identifier: 10.12775/TMNA.2018.038

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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