A Nonconvex Scalar Conservation Law with Trilinear Flux
نویسندگان
چکیده
The focus of this paper is on traveling wave solutions of the equation u t + f(u) x = u xx + 2 u xxx ; in which the ux function f is trilinear and nonconvex. In particular, it is shown that for combinations of parameters in certain ranges, there are traveling waves that converge as ?! 0 to undercompressive shocks, in which the characteristics pass through the shock. The analysis is based on explicit solutions of the piecewise linear ordinary diierential equation satissed by traveling waves. The analytical results are illustrated by numerical solutions of the Riemann initial value problem, and are compared with corresponding explicit results for the case of a cubic ux function.
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تاریخ انتشار 1998