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Global existence of solutions for weakly coupled systems of semi-linear structurally damped σ-evolution models
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-06-19 , DOI: 10.1080/00036811.2020.1781825
Tuan Anh Dao 1, 2
Affiliation  

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 Lm regularity on the initial data, with m[1,2), we use (LmL2)L2 and L2L2 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 σ1 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.



中文翻译:

半线性结构阻尼σ演化模型弱耦合系统解的全局存在性

摘要

在本文中,我们研究了具有不同功率非线性的半线性结构阻尼σ演化模型的弱耦合系统的柯西问题。通过假设额外大号初始数据的规律性,与[1,2), 我们用(大号大号2)-大号2大号2-大号2估计对应的线性柯西问题的解,以证明小数据的全局(及时)存在 Sobolev 从合适的函数空间对任何半线性模型的弱耦合系统的解σ1δ(0,σ). 此外,不仅用检验函数法表明不存在全局解,而且讨论了当σδ(0,σ)是整数。

更新日期:2020-06-19
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