Guangying Lv

Entire solutions of a diffusive and competitive Lotka?Volterra type system with nonlocal delays

This paper is concerned with the entire solution of a diffusive and competitive Lotka–Volterra type system with nonlocal delays. The existence of the entire solution is proved by transforming the system with nonlocal delays to a four-dimensional system without delay and using the comparing argument and the sub-super-solution method. Here an entire solution means a classical solution defined for all space and time variables, which behaves as two wave fronts coming from both sides of the x-axis.

Nonlinear stability of travelling wave fronts for delayed reaction diffusion equations

This paper deals with the nonlinear stability of travelling wave fronts for delayed reaction diffusion equations. We prove that the travelling wave fronts are exponentially stable to perturbations in some exponentially weighted L∞ spaces, and obtain the time decay rates of by the weighted energy estimate.

Non-uniform dependence for a modified Camassa-Holm system

This paper is concerned with the non-uniform dependence on initial data for a modified Camassa-Holm system. We prove that the solution map of the Cauchy problem of the Camassa-Holm system is not uniformly continuous in Hs(R), s > 1. Moreover, we obtain the similar result for the initial boundary value problem for the Camassa-Holm system.

Blow-up solutions of the general b-equationa)

In this short paper, we consider the b-equation. A new precise blow-up scenario is described and some new results are obtained for the blow-up phenomena.

Positive and unbounded solution of stochastic delayed evolution equations

ABSTRACT This article is concerned with the blowup phenomenon of stochastic delayed evolution equations. We first establish the sufficient condition to ensure the existence of a unique nonnegative solution of stochastic parabolic equations. Then the problem of blow-up solutions in mean Lq-norm, q ⩾ 1, in a finite time is considered. The main aim in this article is to investigate the effect of time delay and stochastic term. A new result shows that the stochastic delayed term can induce singularities.

IMPACTS OF NOISE ON ORDINARY DIFFERENTIAL EQUATIONS

ABSTRACT: In this paper, we consider the impacts of noise on ordinary differential equations. We first prove that the weak noise can change the value of equilibrium and the strong noise can destroy the stability of equilibrium. Then we consider the competition between the nonlinear term and noise term, which shows that noise can induce singularities (finite time blow up of solutions) and that the nonlinear term can prevent the singularities. Besides that, some simulations are given in order to illustrate our results.

Stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity and delay

In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results.