Global existence of weak solutions is established for 1D cross-diffusion systems with arbitrary advections via vanishing-viscosity limit and a three-entropy compensated-compactness argument that exploits oscillation correlation.
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A new high-order FEM for linear fourth-order elliptic problems that is nodally bound-preserving and mass-conservative via variational inequality, extended to nonlinear parabolic equations with the same properties.
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Global solutions to cross-diffusion systems with independent advections in one dimension
Global existence of weak solutions is established for 1D cross-diffusion systems with arbitrary advections via vanishing-viscosity limit and a three-entropy compensated-compactness argument that exploits oscillation correlation.
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A high-order nodally bound-preserving and mass-conservative method for linear fourth-order elliptic problems and its applications to nonlinear parabolic equations
A new high-order FEM for linear fourth-order elliptic problems that is nodally bound-preserving and mass-conservative via variational inequality, extended to nonlinear parabolic equations with the same properties.