I want to solve the coupled system $$u_t = f(u,u_x,u_{xx})$$ $$v_t = g(u,u_x,u_{xx}, v, v_x, v_{xx})$$ with $f$ and $g$ such that the right hand sides are linear with respect to their arguments.
I am aware that the Ladyzenskaja book covers this, but the notation and typesetting is horrible and I don't want to use it. Can anyone recommend me a more modern book that treats this kind of PDEs?
I just want an existence/uniqueness result in Hölder spaces.
Thanks a lot.
