# Source for Theory of Linear Transport equations

I'm looking for a source, like a textbook or something else that be used as a reference in a paper, for the theory of linear transport equations.

I want to have a proof of the well-known result that shows that the solution of these equations is given by the initial conditions composed with the solution of the characteristic system of ODEs.

All the results I need are for example perfectly represented in chapter 2 of here. But unfortunately, that are just online lecture notes that I don't want to cite in a paper.

• The Cauchy Problem in Kinetic Theory by Robert T. Glassy published in SIAM covers a lot about the Vlasov equation in the linear and nonlinear cases. – Dayton Jan 16 at 22:07
• Thanks for the answer. I haven't found the basic theorems of chapter 2 in there and I think this book is already too advanced. To clarify I'm not interested in Vlasov equations, but just the existence theory for linear transport equations with variable coefficients – taylor123123 Jan 16 at 22:29

Maybe you are looking for a PDE book which addresses the method of characteristics for (linear) scalar first-order equations in $$n$$ variables. There are few of them that could be used: