Mathematical results for a model of diffusion and precipitation of chemical elements in solid matrices. (English) Zbl 1074.35048

The model studied by the author is a system of strongly coupled quasilinear equations of parabolic type of the form \[ u_t+{\mathcal A}(u)u=f(\cdot,u,\text{grad}\, u)\quad \text{in }\Omega\times (0,\infty) \] with the boundary condition \[ {\mathcal B}(u)u=0\quad \text{on }\partial\Omega\times (0,\infty). \] Existence and uniqueness of the state of local thermodynamic equilibrium are established. Moreover, the author proposes an improved version of the original model for which the general theory of H. Amann can be applied to derive the local existence and smoothness of the corresponding initial value-boundary problem.


35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K57 Reaction-diffusion equations
Full Text: DOI


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