Entropy Solutions

This chapter is devoted to the concept of weak entropy solution. We give the definition of distributional solution and prove that a shock is a distributional solution if and only if the Rankine-Hugoniot Condition holds. We then provide the definition of entropy solution and prove a necessary and sufficient condition for a shock to be an entropy solution. We conclude the chapter with the Kružkov Theorem stating the uniqueness and stability the entropy solution of a Cauchy problem.