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Asymptotic Behaviors of Global Solutions to Fourth-order Parabolic and Hyperbolic Equations with Dirichlet Boundary Conditions
Wenlong Wu, Yanyan Zhang
This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micr…
Well-posedness and asymptotic behavior of solutions to a second order nonlocal parabolic MEMS equation
Yufei Wei, Yanyan Zhang
We consider a second-order nonlocal parabolic MEMS equation with Dirichlet boundary conditions: \[ u_t-Δu=\fracλ{(1-u)^2\bigl(1+\int_Ω\frac{1}{1-u}\,dx\bigr)^2},\quad x\inΩ,\ t>0,…
Asymptotic Behavior of Rupture Solutions for the Elliptic MEMS Equation with Hénon-Type and External Pressure Terms
Yunxiao Li, Yanyan Zhang
This paper investigates an elliptic MEMS-Type equation with Henon and external pressure terms: Delta u = lambda|x|^alpha / u^p + F for x in R^N \ {0}, with u(0)=0 and u>0 for x in…
Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption
Jie Jiang, Philippe Laurençot, Yanyan Zhang
Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells…
Asymptotic and Quenching Behavior for a family of Parabolic System with General Singular Nonlinearities
Qi Wang, Yanyan Zhang
This study is concerned with a family of parabolic system with general singular nonlinearities, which is a generalization of MEMS system. To some extent, the classification of glob…
Singular Behavior of an Electrostatic--Elastic Membrane System with an External Pressure
Yujin Guo, Yanyan Zhang, Feng Zhou
We analyze nonnegative solutions of the nonlinear elliptic problem , where and , on a bounded domain of () with a…