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February 2022 Critical curve for a weakly coupled system of semilinear σ-evolution equations with frictional damping
Tuan Anh Dao, Nguyen Hai Son
Rocky Mountain J. Math. 52(1): 299-321 (February 2022). DOI: 10.1216/rmj.2022.52.299

Abstract

We are interested in studying the Cauchy problem for a weakly coupled system of semilinear σ-evolution equations with frictional damping. The main purpose of this paper is two-fold. We would like to not only prove the global (in time) existence of small data energy solutions but also indicate the blow-up result for Sobolev solutions when σ is assumed to be any fractional number. Moreover, some further generalizations will be also discussed in the present paper.

Citation

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Tuan Anh Dao. Nguyen Hai Son. "Critical curve for a weakly coupled system of semilinear σ-evolution equations with frictional damping." Rocky Mountain J. Math. 52 (1) 299 - 321, February 2022. https://doi.org/10.1216/rmj.2022.52.299

Information

Received: 2 November 2020; Revised: 10 May 2021; Accepted: 13 May 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.299

Subjects:
Primary: 35B33 , 35L56 , 35S05

Keywords: Critical exponent , frictional damping , global existence , weakly coupled system , σ-evolution equation

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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