Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
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We consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time-asymptotically. The hyperbolic model may be viewed as isentropic Euler equations with friction term added to the momentum equation to model gas flow through a porous media. In this case our result justifies Darcy's law time-asymptotically. Our model may also be viewed as an elastic model with damping.
KeywordsNeural Network Porous Medium Nonlinear Dynamics Parabolic Equation Euler Equation
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