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Zbl 0814.35054
Biler, Piotr; Hebisch, Waldemar; Nadzieja, Tadeusz
The Debye system: Existence and large time behavior of solutions. (English)
[J] Nonlinear Anal., Theory Methods Appl. 23, No.9, 1189-1209 (1994). ISSN 0362-546X

The authors study the so-called Debye system: $$u\sb t = \nabla \cdot (\nabla u - u \nabla \varphi), \quad v\sb t = \nabla \cdot (\nabla v + v \nabla \varphi)$$ (coupled through $\varphi$ satisfying $\Delta \varphi = u - v)$ in a bounded domain $\Omega \subset \bbfR\sp n$ with smooth boundary and no flux boundary conditions. Conditions for local and global existence and uniqueness of weak solutions are given in several space dimensions $n$. For $n = 2,3$ it is shown that a weak solution of the system above converges to the (unique) stationary solution if $t\to\infty$.
[R.Manthey (Jena)]

MSC 2000:: *35K60 (Nonlinear) BVP for (non)linear parabolic equations
35D05 Existence of generalized solutions of PDE

Keywords: Debye system; local and global existence; uniqueness

Cited in: Zbl 1181.35170 Zbl 0976.82046

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