TY - JOUR T1 - On the critical behavior in nonlinear evolutionary PDEs with small viscocity JF - Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460 Y1 - 2012 A1 - Boris Dubrovin A1 - Maria Elaeva AB - We address the problem of general dissipative regularization of the quasilinear transport equation. 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, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically. PB - SISSA UR - http://hdl.handle.net/1963/6465 U1 - 6409 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER -