具有椭圆性质的耗散非线性发展方程组解的渐近行为(英文)

Asymptotic Behavior of Solutions to Dissipative Nonlinear Evolution Equations with Ellipticity

讨论了如下具有椭圆性质的耗散非线性发展方程组Cauchy问题解的整体存在性和渐近行为:ψt=-(1-α)ψ-θx+αψxx,θt=-(1-α)θ+υψx+2ψθx+αθxx,具有初值(ψ,θ),(x,0)=(ψ0(x),θ0(x))→(ψ±,θ±),x→±∞,其中α和υ是正常数且满足条件:α<1,υ<α(1-α).

In this paper, we study the global existence and the asymptotic behavior of the solutions to Cauchy problem for the following nonlinear evolution equations with ellipticityψt=-(1-α)ψ-θx+αψxx, θt=-(1-α)θ+υψx+2ψθx+αθxx,with initial data(ψ,θ)(x,0)=(ψ0(x),θ0(x))→(ψ±,θ±), x→±∞,where α and υ are positive constants such that α<1, υ<α(1-α).