Asymptotic Behavior of Multidimensional Scalar Relaxation Shocks

Details Asymptotic Behavior of Multidimensional Scalar Relaxation Shocks Asymptotic Behavior of Multidimensional Scalar Relaxation Shocks

2008-09-24

arxiv.org/abs/0809.4084v1

Mathematics

Analysis of PDEs

58 pages

Scientific paper

We establish pointwise bounds for the Green function and consequent linearized stability for multidimensional planar relaxation shocks of general relaxation systems whose equilibrium model is scalar, under the necessary assumption of spectral stability. Moreover, we obtain nonlinear $L^{2}$ asymptotic behavior/sharp decay rate of perturbed weak shocks of general simultaneously symmetrizable relaxation systems, under small $L^{1}\cap H^{[d/2]+3}$ perturbations with first moment in the normal direction to the front.

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