Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions
Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions
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DOI：
10.1016/j.jmaa.2017.02.008
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发表时间：
2017-02
影响因子：
1.3
通讯作者：
F. Cordoni;L. D. Persio
中科院分区：
文献类型：
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作者：
F. Cordoni;L. D. Persio
我们考虑在动态边界条件下的网络上的反应扩散方程，具有时间延迟行为，也允许乘法高斯噪声扰动。利用半群理论，我们将上述随机问题改写为一个抽象的在合适积Hilbert空间中取值的随机偏微分方程，并证明了其温和解的存在唯一性。最后，研究了随机最优控制的应用。
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behavior, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the aforementioned stochastic problem as an abstract stochastic partial differential equation taking values in a suitable product Hilbert space, for which we prove the existence and uniqueness of a mild solution. Eventually, a stochastic optimal control application is studied.