Global Well-Posedness and Polynomial Decay for a Nonlinear Viscoelastic Equation with Variable Density and Memory
Rongjiang Fu *
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China.
*Author to whom correspondence should be addressed.
Abstract
Aims: This paper investigates a nonlinear viscoelastic equation with variable density and memory.
Study Design: Polynomial decay.
Place and Duration of Study: This paper was completed at the School of Mathematics and Statistics at Southwest University during from May 2024 to February 2025.
Methodology: Using Faedo-Gal¨erkin method and Energy method.
Results: We study the global well-posedness and show the polynomial decay results with more general and weaker assumptions (compared with the previous studies) on the memory kernel.
Conclusion: We study the well-posedness and polynomial stability, which is different from others, where the multiplying method and energy method were used to study the polynomial stability. This result substantially improves earlier results in the literature.
Keywords: Viscoelastic equation, variable density, memory kernel, global weak solutions, polynomial decay