Existence and stability results of nonlinear swelling equations with logarithmic source terms

被引：1
作者：
Kafini, Mohammad [1 ,2 ]
Al-Gharabli, Mohammad M. [1 ,2 ]
Al-Mahdi, Adel M. [1 ,2 ]
机构：
[1] King Fahd Univ Petr & Minerals, Dept Math, Dhahran 31261, Saudi Arabia
[2] King Fahd Univ Petr & Minerals, Interdisciplinary Res Ctr Construct & Bldg Mat, Dhahran 31261, Saudi Arabia
来源：
AIMS MATHEMATICS | 2024年 / 9卷 / 05期
关键词：
swelling system; Faedo-Galerkin method; well-depth method; logarithmic Sobolev inequality; variable exponents; general decay; POROUS ELASTIC SOILS; WAVE-EQUATION; EXPONENTIAL STABILITY; VARIABLE EXPONENT; GLOBAL EXISTENCE; CONTINUUM THEORY; PLATE EQUATION; BLOW-UP; DECAY; SYSTEM;
D O I：
10.3934/math.2024627
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We considered a swelling porous-elastic system characterized by two nonlinear variable exponent damping and logarithmic source terms. Employing the Faedo-Galerkin method, we established the local existence of weak solutions under suitable assumptions on the variable exponents functions. Furthermore, we proved the global existence utilizing the well-depth method. Finally, we established several decay results by employing the multiplier method and the Logarithmic Sobolev inequality. To the best of our knowledge, this represents the first study addressing swelling systems with logarithmic source terms.
引用
收藏
页码：12825 / 12851
页数：27
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