Hongjun Gao

Global existence and decay for the semilinear thermoelastic contact problem

In this paper a class of semilinear thermoelastic contact problems is considered and the existence and exponential decay of the weak solutions are obtained.

On a coupled Kuramoto–Sivashinsky and Ginzburg–Landau-type model for the Marangoni convection

The surface tension driven Marangoni convection is an interesting pattern formation system. The “primitive” governing equations are too complicated to be investigated analytically. In this paper, the authors consider a simplified model for this system. This simplified model is in the form of coupled Kuramoto-Sivashinsky and Ginzburg-Landau type partial differential equations. The authors prove the existence and uniqueness of global solutions of this simplified mathematical model under the condition that the Marangoni number Ma>Mac+k/25, where Mac is the critical Marangoni number at which the trivial stationary state becomes linearly unstable, and k is a positive constant related to other system parameters. The authors use the contraction mapping principle in the proof. This work sets the foundation for further study of this model.

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

The generalized Ginzburg-Landau equation: posed in a quarter plane

This paper is concerned with a generalized 1D Ginzburg-Landau equation involving a fifth order term and two nonlinear terms containing spatial derivatives. The equation is posed in a quarter plane 0=