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2.00 pm, Lecture Hall 803 KdV-type nonlinear dispersive regularization of gas dynamics Sonakshi Sachdev Chennai Mathematical Institute. 10-04-19 Abstract KdV is the simplest prototype for conservative regularization of shock-like singularities in 1D. Unlike the dissipative Burgers' equation, it is a dispersive regularization of the Hopf equation $u_t + u u_x = 0$. KdV is a universal equation describing the dynamics of a single field which, depending on context, may be the surface height of waves in shallow water or blood pressure in an artery etc. For a more complete treatment of compressible gas dynamics one needs a multi-field generalization that simultaneously describes the evolution of density, velocity, pressure and entropy. Here, we present such a generalization of KdV to adiabatic gas dynamics. Like KdV, this regularized gas dynamics admits Lagrangian and Hamiltonian-Poisson bracket formulations, as well as families of solitary and periodic traveling waves. Numerical solutions of the IVP are presented and compared with the unregularized and viscous models. Numerical evidence suggests soliton-like scattering and recurrent behaviour in a bounded domain.
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