STABILITY OF STATIONARY SOLUTIONS FOR A SCALAR NON-LOCAL REACTION-DIFFUSION EQUATION
STABILITY OF STATIONARY SOLUTIONS FOR A SCALAR NON-LOCAL REACTION-DIFFUSION EQUATION
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DOI：
10.1093/qjmam/48.4.557
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发表时间：
1995-11
影响因子：
0.9
通讯作者：
Pedro Frettas
中科院分区：
文献类型：
--
作者：
Pedro Frettas
研究了具有齐次Neumann边界条件的非局部反应扩散方程u1 = uxx + f（u）-a1 × 10 f（u）dx的平稳解的稳定性.依赖于α，给出了定常解的不稳定流形的维数的界.特别是，它表明，只有常数或单调固定的解决方案可能是稳定的。对于一个特殊的情况下，一个三次一样的f，存在的Hopf分支被证明。最后讨论了有关的方程。
The stability of stationary solutions of the non-local reaction-diffusion equation u 1 = u xx + f (u) - a ∫ 1 0 f(u)dx with homogeneous Neumann boundary conditions is studied. Depending on α, bounds on the dimension of the unstable manifold of a stationary solution are given. In particular, it is shown that only constant or monotone stationary solutions may be stable. For the specific case of a cubic like f, the existence of a Hopf bifurcation is proven. Finally, some related equations are discussed.