Recently, Professor Guo Zhenhua from the School of Mathematics at Guangxi University (GXU), in collaboration with scholars including Hou Meichen from Northwest University, Qiu Guiqin from Fuzhou University, and Xu Lingda from the Hetao Research Institute of Mathematics and Interdisciplinary Sciences (Shenzhen), has made new progress in the field of stability of composite waves in nonlinear viscoelastic systems. The research results, titled "Asymptotic Stability of the Composite Wave of Rarefaction Wave and Contact Wave to Nonlinear Viscoelasticity Model with Non-convex Flux," were published in the international mathematics journal Archive for Rational Mechanics and Analysis. Guo Zhenhua is the first author, and GXU is the primary affiliation for the paper.

This study focuses on nonlinear viscoelastic dynamical systems with memory effects. Unlike the convex flux functions in traditional gas dynamics, the stress-strain relationship of viscoelastic materials exhibits significant non-convex characteristics, posing huge challenges to theoretical analysis and modeling. Focusing on the "rarefaction wave + contact discontinuity" composite wave pattern, the research team innovatively constructed an explicit analytical expression for viscous contact waves. By introducing the concept of a "viscous connecting surface" and employing refined domain decomposition energy estimation methods, they successfully overcame the analytical difficulties caused by non-convexity and rigorously proved the nonlinear asymptotic stability of this type of composite wave. This achievement not only improves the mathematical theory regarding the interaction mechanisms of nonlinear waves in viscoelastic materials but also provides new insights for the study of complex waves in broader hyperbolic-parabolic coupled systems.

The aforementioned research falls within the scope of partial differential equations, which is a core branch of modern mathematics and a key link connecting mathematics with physics, mechanics, and engineering sciences. GXU's partial differential equation and applications team continues to strengthen the construction of its talent pipeline and has now developed into an academic team with significant influence in the domestic and international academic communities. The team deeply engages in research on partial differential equations in fluid mechanics and viscoelastic dynamic equations, achieving a series of original results in the stability analysis of nonlinear waves.