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A doubly nonlinear parabolic equation of the form α(u t) − ∆u + W ′ (u) = f , complemented with initial and either Dirichlet or Neumann homogeneous boundary conditions, is addressed. The two nonlinearities are given by the maximal monotone function α and by the derivative W ′ of a smooth but possibly noncon-vex potential W ; f is a known source. After… (More)

We consider a diffuse interface model for tumor growth recently proposed in [3]. In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a… (More)

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