Weak Solutions and Shock Waves

Among the phenomena of nonlinear propagation, shock wavesShock waves play a particular role. Through a moving front that separates space into two half-spaces, the field variables undergo a discontinuity. To study shock waves, it is necessary to extend the concept of solutions to include the case of discontinuous functions. For this reason, the concept of weak solutionWeak solution is introduced in this chapter. A brief overview of shock wave theory and the issue of nonuniqueness for weak solutions, particularly in the context of the Riemann problemRiemann, will be discussed. As an example of this problem, we will examine shock waves in Euler fluid dynamics and the fluidodynamic model of car traffic.