ASYMPTOTIC SPATIAL HOMOGENEITY OF SOLUTIONS TO CONSERVATION LAWS WITH MEMORY IN SEVERAL SPACE DIMENSIONS

摘要

We prove that any solution of the problem (u + K*u)(t) + Sigma a(i)(u)u(xi) = 0 on (0, infinity) x R-N with spatially periodic initial data converges to a constant provided some non-degeneracy conditions on the kernel K and the non-linear functions a(i),i = 1,..., N are imposed. (C) 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd. [References: 13]