Before proceeding further it is necessary to introduce the concept of a jump condition – a condition that holds at a discontinuity or abrupt change.
Consider a 1D situation where there is a jump in the scalar conserved physical quantity , which is governed by integral conservation law
for any , , , and, therefore, by partial differential equation 
for smooth solutions.
Let the solution exhibit a jump (or shock) at , where  and , then
The subscripts 1 and 2 indicate conditions just  upstream and just downstream of the jump respectively, i.e.  and 
Note, to arrive at equation () we have used the fact that  and .
Now, let  and , when we have  and , and in the limit
where we have defined  (the system characteristic or shock speed), which by simple division is given by
Equation () represents the jump condition for conservation law ().  A shock situation arises in a system where its characteristics intersect, and under these conditions a requirement for a unique single-valued solution is that the solution should satisfy the admissibility condition or entropy condition. For physically real applications this means that the solution should satisfy the Lax entropy condition
where  and  represent characteristic speeds at upstream and downstream conditions respectively.