Existence for evolutionary Neumann problems with linear growth by stability results
Leah Schätzler · Annales Academiae Scientiarum Fennicae Mathematica · 2019
We are concerned with the Neumann type boundary value problem to parabolic systems ∂ t u -div(D ξ f (x, Du)) = -D u g(x, u), where u is vector-valued, f satisfies a linear growth condition and ξ → f (x, ξ) is convex.We prove that variational solutions of such systems can be approximated by variational solutions towith p > 1.This can be interpreted both as a stability and existence result for general flows with linear growth.