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Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations
Authors:Yang Jun  Guan Xinping
Institution:(1) Department of Mathematics and Physics, Yanshan University, 066004 Qinhuangdao
Abstract:This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial functional differential equations of the form

$$\frac{\partial }{{\partial t}}u_i (x,t) - \sum\limits_{k = 1}^n {p_k (t)u_i (x,t - \sigma _k (t))] + A_i (x,t)u_i (x,t) + \sum\limits_{j = 1}^m {B_{ij} (x,t)f_{ij} (u_j (x,t - \tau )) = C_i (t)\Delta u_i (x,t) + \sum\limits_{j = 1}^m {D_{ij} (t)\Delta u_i (x,t - r_j ),i = 1,2,...,m,(x,t) \in \Omega {\text{ x }}(0,\infty ) \equiv G} } } $$
(1)
where Ω is a bounded domain in Rn with piecewise smooth boundary.

$$\Delta u_1 (x,t) = \sum\limits_{j = 1}^n {\left( {\frac{\partial }{{\partial x_j^2 }}^2 } \right)u_1 (x,t),\tau ,r_j  = {\text{ const}}{\text{.}} > 0} $$
(1)
Sufficient conditions are obtained for oscillation of solutions of the systems, these results are illustrated by some examples. The project is supported by Natural Science Foundation of Heilongjiang Province.
Keywords:Parabolic partial differential equation  nonlinear neutral type  system  oscillation
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