My presentation topic is Burgers' equation. My plan is to discuss Burgers' inviscid equation, $u_t+uu_x=0$ and its solution, as well as its solution with particular initial conditions. Then considering the weak solutions to the equation and the Rankine-Hugoniot conditions. Finally, will go over Burgers' viscous equation, $u_t+uu_x= \epsilon u_{xx}$ and some examples of scenarios in which Burgers' equation is used - namely traffic flow and gas dynamics.
