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Applied Math Seminar
Weakly nonlinear waves in a relaxing gas
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We obtain transport equations describing asymptotic behavior of nonlinear waves propagating through a material medium exhibiting mixed nonlinearity. The effects of genuine nonlinearity leading to the distortion of the wave profile and subsequent shock formation are studied. Asymptotic decay laws influenced by the weak dissipative mechanisms such as stratification, relaxation and non-planar flow configurations are obtained. Transport equations are derived for signals having all possible wave modes which are mutually coupled and interact resonantly among themselves. Kinematics of a shock of arbitrary strength, which is still an open problem in the literature, is briefly discussed. |