Global Well-Posedness of a Conservative Relaxed Cross Diffusion System

@article{Lepoutre2012GlobalWO,
  title={Global Well-Posedness of a Conservative Relaxed Cross Diffusion System},
  author={Thomas Lepoutre and Michel Pierre and Guillaume Rolland},
  journal={SIAM J. Math. Analysis},
  year={2012},
  volume={44},
  pages={1674-1693}
}
We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form ui → ∂tui − ∆(ai(ũ)ui) where the ui, i = 1, ..., I represent I density-functions, ũ is a spatially regularized form of (u1, ..., uI) and the nonlinearities ai are merely assumed to be continuous and bounded from below. Existence of global weak solutions is obtained in any space dimension. Solutions are proved to be regular and unique when the ai are locally… CONTINUE READING

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