A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise
A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise
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DOI：
10.1007/s004400100153
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发表时间：
2001-11
影响因子：
2
通讯作者：
S. Albeverio;Z. Haba;F. Russo
中科院分区：
文献类型：
--
作者：
S. Albeverio;Z. Haba;F. Russo
研究了有界体积中受白噪声扰动的二维热方程。方程被λ：F(AU)：类型的非线性摄动，其中：：表示关于自由解的Wick(Re)序；λ，A是小参数，表示解，f是具有紧支集的复测度的傅里叶变换.证明了一类广义函数的解的存在唯一性.给出了解的一个显式构造，并证明了当A足够小时，λ中的级数展开式的每一项都与一个L2值测度相联系。
A two-space dimensional heat equation perturbed by a white noise in a bounded volume is considered. The equation is perturbed by a non-linearity of the type λ :f(AU) :, where :: means Wick (re)ordering with respect to the free solution;λ,Aare small parameters,Udenotes a solution,fis the Fourier transform of a complex measure with compact support.Existence and uniqueness of the solution in a class of Colombeau-Oberguggenberger generalized functions is proven. An explicit construction of the solution is given and it is shown that each term of the expansion in a power series in λ is associated with anL2-valued measure whenAis a small enough.