On the critical behavior in nonlinear evolutionary PDEs with small viscosity
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The problem of general dissipative regularization of the quasilinear transport equation is studied. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function; this statement generalizes a result of Il’in . We provide some analytic arguments supporting the conjecture and test it numerically.
KeywordsMathematical Physic Cauchy Problem Shock Front Asymptotic Formula Burger Equation
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