| Abstract: |
| Phase separation has recently become a paradigm in Cell Biology. A phase-field model describing the formation of protein-RNA complexes subject to phase segregation is examined. The dynamics involve a single protein, two RNA species, and two complexes. Protein and RNA species are governed by coupled reaction-diffusion equations which also depend on the two complexes. The latter ones are driven by two Cahn-Hilliard equations with singular potentials and reaction terms depending on the solution variables. Some selected modeling and analytic features of the system are discussed. Among the several technical difficulties, the most remarkable one arises from the fact that the two complexes are initially nonexistent, so their initial conditions are zero, i.e., they start from a pure phase: this is a major obstacle in handling the Cahn-Hilliard equation with source term due to the singular nature of the considered potentials. The existence of weak solutions is established in both two and three dimensions. |
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