报告题目：The physical motivation behind some mathematical studies

报 告 人：王美燕 (Master Student @ DUT - Dalian University of Technology)

报告时间：2026年4月16日（星期四）9:00—9:45

报告地点：数学科学学院114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

Abstract: This talk is about a physical motivation for the damping term $u_{xxt}$. The first part presents the explicit capillary pressure relation $p^n - p^w = p^c - \tau \dot{S}^w$ in multiphase porous media flow, as formulated by Hassanizadeh and Gray, highlighting its derivation from conservation laws and the secondlaw of thermodynamics; the second part presents microforce balance framework, which yields the generalized Ginzburg-Landau and Cahn-Hilliard equations by introducing constitutive relations and the local dissipation inequality; the final part is connected with the theory of Rivlin-Ericksen fluids and for an incompressible second-order fluid undergoing nonsteady simple shearing flow between parallel plates the equation reduces to the linear third-order PDE $u_t = u_{xx} - u_{xxt}$ on a strip. These examples illustrate how fundamental physical laws guide the development of mathematical models across multiphase flow, phase-field theory, and non-Newtonian fluid mechanics.