具有非线性阻尼项的p-方程组非线性扩散波的Lp-衰减率

讨论了具有非线性阻尼项的p-方程组的Cauchy问题解的L^p(2≤ p≤ +∞) 收敛率. 具体地说, 当相应的初始扰动(w₀(x), z₀(x))Î(H³´ H²)(R), 并且|v₊-v_-|+||w₀||₃+||z₀||₂充分小时, 对应的Cauchy问题存在唯一的整体解(v(x,t), u(x,t)), 并且依时间渐近收敛到由Darcy定律得到的非线性扩散波. 此外, 还得到了解的L^p(2≤ p≤ +∞)收敛率.     

THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.     

ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR GENERALIZED BURGERS EQUATION

This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u , the authors prove the existence of the global smooth solution to the Cauchy problem (I), also find the solution u(x, t) to the Cauchy problem (I) satisfying sup |u(x, t) -uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgersequation ut f(u)x = 0 with Riemann initial data u(x, 0) =