Yuanwei Qi

Existence and non-existence of global solutions of diffusion systems with nonlinear boundary conditions

for 1 i n, where Ω ⊂ R is a bounded domain with smooth boundary ∂Ω, η is the unit outward normal vector on ∂Ω, the exponents mi are positive and indices mij are non-negative, i, j = 1, . . . , n. In addition, initial data ui0(x) ∈ C1(Ω̄), (1 i n) are positive functions and satisfy the compatibility conditions. When n = 1, we have the familiar equation (u)t = ∆u, or vt = ∆v1/m. It is clear that m > 1 corresponds to the fast diffusion equation, whereas m < 1 the

The global dynamics of isothermal chemical systems with critical nonlinearity

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u1,t = u1,xx − uα1 uβ2, u2,t = du2,xx + uα1 uβ2 with non-negative initial data, where the exponents α,β satisfy 1 0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x|→∞. We show the exact large time behaviour of solutions which is universal.

Self-similar singular solutions of a p-Laplacian evolution equation with absorption ☆

We consider, for pAð1; 2Þ and q > 1; self-similar singular solutions of the equation vt ¼ divðjrvj p� 2 rv Þ� v q in R n �ð 0; NÞ; here by self-similar we mean that v takes the form

Asymptotics of minimizers of variational problems involving curl functional

In this paper we are concerned with singularly perturbed variational problems involving the curl functional, which arise in the mathematical theory of liquid crystals. The asymptotic behavior of the minimizers in the singular limiting process is discussed, which is closely related to the variational problems for curl functional under various constraints.

Singular solutions of parabolic

We consider, for and , the -Laplacian evolution equation with absorption We are interested in those solutions, which we call singular solutions, that are non-negative, non-trivial, continuous in , and satisfy for all . We prove the following: (i) When , there does not exist any such singular solution. (ii) When , there exists, for every , a unique singular solution that satisfies as . Also, as , where is a singular solution that satisfies as . Furthermore, any singular solution is either or for some finite positive .

p

Abstract In this paper we study the global stability of diffusive predator–prey system of Holling–Tanner type in a bounded domain Ω ⊂ R N with no-flux boundary condition. By using a novel approach, we establish much improved global asymptotic stability of the unique positive equilibrium solution than works in literature. We also show the result can be extended to more general type of systems with heterogeneous environment.

-Laplacian with absorption

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system

The global self-similarity of a chemical reaction system with critical nonlinearity

u_{1,t}=u_{1,xx}-u_1u^{2}_2,\qquad u_{2,t}=du_{2,xx}+u_1u^{2}_2