Some results for a weakly coupled system of semi-linear structurally damped σ-evolution equations

• Autorzy: Dao Tuan Anh , Said Khaldi

Identyfikatory

DOI

10.1515/jaa-2023-0099

• Języki publikacji: EN

Abstrakty

EN

In this paper, we are interested in studying the Cauchy problem for a weakly coupled system of two semi-linear structurally damped σ_k-evolution equations, where σ_k ≥ 1 for k = 1, 2. Our first purpose involves the proof of global (in time) existence of small data energy solutions by mixing additional L^mk regularity for the data, where m_k ∈ [1, 2). We want to point out that in some cases of choosing suitable parameters m_k, with k = 1, 2, the obtained lower bound of one exponent p or q related to power nonlinearities on the right-hand sides is really smaller than the critical exponent, the so-called modified Fujita exponent. The second aim of this paper is to discuss a blow-up result for Sobolev solutions with any different fractional values of σ_k ≥ 1 when m₁ = m₂.

Słowa kluczowe

EN

weakly coupled system; sigma-evolution equation; structural damping; global existence; blow-up

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2024
• Tom: Vol. 30, nr 2
• Strony: 271--288
• Opis fizyczny: Bibliogr. 25 poz., 1 wykr.

Twórcy

autor

Dao Tuan Anh

• Faculty of Mathematics and Informatics, Hanoi University of Science and Technology, No. 1 Dai Co Viet road, Hanoi, Vietnam

• https://orcid.org/0000-0003-4578-4235

autor

Said Khaldi

• Laboratory of Analysis and Control of PDEs, Djillali Liabes University, P. O.Box 89, Sidi Bel Abbes 22000, Algeria

Bibliografia

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