Global existence of solutions for weakly coupled systems of semi-linear structurally damped σ-evolution models. Issue 4 (4th March 2022)

• Record Type: Journal Article
• Authors: Anh Dao, Tuan
• Is Part Of: Applicable analysis. Volume 101:Issue 4(2022)
• Page Start: 1396
• Page End: 1429
• Publication Date: 2022-03-04
• Subjects: Structurally damped σ-evolution equations -- weakly coupled systems -- global existence -- loss of decay -- Harmonic analysis -- critical exponent; 35L30 -- 35L56 -- 35S05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1781825
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study the Cauchy problems for weakly coupled systems of semi-linear structurally damped σ -evolution models with different power nonlinearities. By assuming additional L m regularity on the initial data, with m ∈ [ 1, 2 ), we use ( L m ∩ L 2 ) − L 2 and L 2 − L 2 estimates for solutions to the corresponding linear Cauchy problems to prove the global (in time) existence of small data Sobolev solutions to the weakly coupled systems of semi-linear models from suitable function spaces for any σ ≥ 1 and δ ∈ ( 0, σ ) . Moreover, not only the nonexistence of global solution is indicated by using test function method, but also a lifespan estimate is discussed when σ and δ ∈ ( 0, σ ) are integers.