How to solve coupled linear 1st order PDE
It is fairly straight forward to solve linear 1st order PDEs by the method of characteristics. For example, if
we have that on the characteristic curve of . From this we deduce that where .
Now, how does this work when is multidimensional. Can I solve equations on the following form by characteristics, or by any other means?
where the components of and might be dependent on and .
In particular, I am trying to solve the following,
where and are functions of and , where , . Any help is highly appreciated.