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- W3021822334 abstract "We consider a diffuse interface model of tumor growth proposed by A. Hawkins-Daruud et al. This model consists of the Cahn-Hilliard equation for the tumor cell fraction φ nonlinearly coupled with a reaction-diffusion equation for ψ which represents the nutrient-rich extracellular water volume fraction. The coupling is expressed through a suitable proliferation functionp(φ) multiplied by the differences of the chemical potentials for φ and ψ. The system is equipped with no-flux boundary conditions which entails the conservation of the total mass, that is, the spatial average of φ+ψ. Here we prove the existence of a weak solution to the associated Cauchy problem, provided that the potential F and p satisfy sufficiently general conditions. Then we show that the weak solution is unique and continuously depends on the initial data, provided that p satisfies slightly stronger growth restrictions. Also, we demonstrate the existence of a strong solution and that any weak solution regularizes in finite time. Finally, we prove the existence of the global attractor in a phase space characterized by an a priori bounded energy." @default.
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- W3021822334 date "2014-05-29" @default.
- W3021822334 modified "2023-09-23" @default.
- W3021822334 title "On a diffuse interface model of tumor growth" @default.
- W3021822334 doi "https://doi.org/10.34657/2787" @default.
- W3021822334 hasPublicationYear "2014" @default.
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