补偿列紧理论与一个六阶奇异扰动偏微分方程解的收敛性

COMPENSATED COMPACTNESS AND CONVERGENCE OF A SINGULAR PERTURBED SIXTH ORDER PARTIAL DIFFERENTIAL EQUATIONS

用补偿列紧理论得到了如下形式的六阶奇异扰动偏微分方程u_t+f_x(u)-δu_(xxxxxx)=εu_(xx)的解{u_~δ}当δ→O^+,ε→O^+时的收敛性。

We study the convergence of solutions {u_(?)~δ} for the partial differential equation of the formu_t+f_x(u)-δu_(xxxxxx)=εu_(xx)as ε and δ approach zero, where the flux function f is smooth and nonlinear (but not necessary convex). Using an argument derived from the method of compensated compactness, we prove that if the higher order viscosity parameter δ is small enough to the dissipation parameter ε, then there exists a subsequence of the solutions {u_(?)~δ} which converges pointwise almost everywhere to the generalized solution of the limit hyperbolic conservation law.