Department of Mathematics, Faculty of Science, Mansoura University, Egypt
http://dx.doi.org/10.1016/j.joems.2014.10.005
Abstract
t In this paper we derive rigorously the amplitude equation, using the natural separation of time-scales near a change of stability, for the stochastic generalized Swift–Hohenberg equation with quadratic and cubic nonlinearity in this form du ¼ ð1 þ @2 xÞ 2 u þ meu þ cu2 u3 h idt þ redW; where WðtÞ is a Wiener process. For deterministic PDE it is known that the quadratic term generates an additional cubic term, which is unstable. We consider two cases depending on c2. If c2 < 27 38, then we have amplitude equation with cubic nonlinearities. In the other case c2 ¼ 27 38 the cubic term in the amplitude equation vanishes. Therefore we consider larger solutions to obtain an amplitude equation with quintic nonlinearities.
Mohammed, W. W. (2015). Stochastic amplitude equation for the stochastic generalized Swift–Hohenberg equation. Journal of the Egyptian Mathematical Society, 23(3), 482-489. doi: http://dx.doi.org/10.1016/j.joems.2014.10.005
MLA
Wael W. Mohammed. "Stochastic amplitude equation for the stochastic generalized Swift–Hohenberg equation", Journal of the Egyptian Mathematical Society, 23, 3, 2015, 482-489. doi: http://dx.doi.org/10.1016/j.joems.2014.10.005
HARVARD
Mohammed, W. W. (2015). 'Stochastic amplitude equation for the stochastic generalized Swift–Hohenberg equation', Journal of the Egyptian Mathematical Society, 23(3), pp. 482-489. doi: http://dx.doi.org/10.1016/j.joems.2014.10.005
VANCOUVER
Mohammed, W. W. Stochastic amplitude equation for the stochastic generalized Swift–Hohenberg equation. Journal of the Egyptian Mathematical Society, 2015; 23(3): 482-489. doi: http://dx.doi.org/10.1016/j.joems.2014.10.005
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