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If a PDE has a unique classical solution, must it have a unique viscosity solution? The particular problem I am interested in is parabolic, but I would be interested in the general case. A short ...

Consider the following parabolic equation: $$\DeclareMathOperator{\Div}{div} \begin{cases} \dfrac{\partial \rho }{\partial t}-\Div\left( a\left( x\right) \nabla \rho \right) +p(x)\rho = 0 & \...

I am looking for a reference wherein existence and uniqueness results are proven for a system of PDEs of the form $$ \frac{\partial Q}{\partial t} + A \frac{\partial Q}{\partial x} = f(Q,x,t) + \frac{...