Pointwise estimates and \(L_p\) convergence rates to diffusion waves for \(p\)-system with damping.
The authors are interested in the large time behavior of the solution of Cauchy problem for the \(p\)-system with frictional damping (\(2 \times 2\) system of conservation laws with linear right-hand side). New approximate Green functions with a parameter is introduced and investigated by Fourier analysis. The new pointwise estimates on the solutions are obtained such that the optimal \(L_p\) convergence to the nonlinear diffusion waves can be deduced.
scientific article; zbMATH DE number 1884224