Answer to Question #169678 in Differential Equations for Gp

Question

Find conditions under which a scalar conservation law can have a stationary jump discontinuity.

Answer 1

A general form of scalar conservation laws with further properties including some basic models and provide examples of computational methods for them. The equations described by

$∂_tu+∂_xf(u)=0$ , t>0, x∈R

in one dimension are known as scalar conservation laws where u=u(t,x) is the conserved quantity

and f=f(u) is the associated flux function depending on t and x.

The jump condition with discontinuous flux function can be given as

$x'(t) = S(u^{x+}, u^{x-})$