A phase-field model couples viscoelastic compressible tumor mechanics to nutrient diffusion and predicts symmetry-breaking instabilities from elastic buckling and apoptosis-driven volume loss.
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Existence and uniqueness of weak solutions are proved for the semilinear time-dependent equation with second or fourth order diffusion and cubic nonlinearity, for both smooth and rough initial data via Faedo-Galerkin and compactness methods.
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A phase-field model for viscoelastic compressible tumor growth
A phase-field model couples viscoelastic compressible tumor mechanics to nutrient diffusion and predicts symmetry-breaking instabilities from elastic buckling and apoptosis-driven volume loss.
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Well-posedness and regularity for seminlinear time-dependent second and fourth order in space equations
Existence and uniqueness of weak solutions are proved for the semilinear time-dependent equation with second or fourth order diffusion and cubic nonlinearity, for both smooth and rough initial data via Faedo-Galerkin and compactness methods.