Total variation estimate for hyperbolic systems - #499
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This PR formalizes (the statement of) an a priori estimate for the total variation norm of solutions to viscous hyperbolic systems, as established in [1]. This estimate is crucial for proving that vanishing viscosity solutions converge to unique entropy solutions.
The estimate is elementary to state but very challenging to prove, which is why I believe it is a good benchmark problem for the development of formalization for nonlinear PDE.
To avoid technical details, the estimate is stated for global smooth solutions. However, this qualitative smoothness preserves all the difficulty of establishing the theorem, which is quantitative in nature.
[1]. Bianchini and Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems. Annals of Mathematics 161 (2005).