We consider a Cauchy problem for a strictly hyperbolic, $N\times N$ quasilinear system in one space dimension $u_t+A(u) u_x=0$, where the matrix valued map $A$ is smooth and with non genuinely nonlinear characteristic fields. We introduce a Glimm type functional, quadratic in the sizes of waves whose strengths are smaller than some fixed threshold parameter. Next, we investigate the rate of convergence of approximate solutions constructed via the Glimm scheme. Moreover, we give a conjecture on the rate of convergence without any additional assumption on $A$ beyond the strict hyperbolicity and $\mathcal{C}^2$ regularity.

On the convergence rate for the Glimm scheme

ANCONA, FABIO;MARSON, ANDREA
2009

Abstract

We consider a Cauchy problem for a strictly hyperbolic, $N\times N$ quasilinear system in one space dimension $u_t+A(u) u_x=0$, where the matrix valued map $A$ is smooth and with non genuinely nonlinear characteristic fields. We introduce a Glimm type functional, quadratic in the sizes of waves whose strengths are smaller than some fixed threshold parameter. Next, we investigate the rate of convergence of approximate solutions constructed via the Glimm scheme. Moreover, we give a conjecture on the rate of convergence without any additional assumption on $A$ beyond the strict hyperbolicity and $\mathcal{C}^2$ regularity.
2009
Hyperbolic Problems: Theory, Numerics, Applications
9780821847299
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2445758
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