A locally quadratic Glimm functional and sharp convergence rate of the Glimm scheme for nonlinear hyperbolic systems
نویسندگان
چکیده
Consider the Cauchy problem for a strictly hyperbolic, N×N quasilinear system in one space dimension ut + A(u)ux = 0, u(0, x) = ū(x), (1) where u 7→ A(u) is a smooth matrix-valued map, and the initial data u is assumed to have small total variation. We investigate the rate of convergence of approximate solutions of (1) constructed by the Glimm scheme, under the assumption that, letting λk(u), rk(u) denote the k-th eigenvalue and a corresponding eigenvector of A(u), respectively, for each k-th characteristic family the linearly degenerate manifold
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