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

Leblond, Jean-Baptiste

Nonlinear Anal., Real World Appl. 6, No. 2, 297-322 (2005).

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.

Reviewer: Sen-Zhong Huang (Hamburg)

MSC:

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

Keywords:

strongly coupled quasilinear equations; local thermodynamic equilibrium; local existence

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