Random attractors for semilinear reaction-diffusion equation with distribution derivatives and multiplicative noise on \(\mathbb{R}^{n}\)

Open Journal of Mathematical Sciences

卷:4

Qiaozhen Ma¹  Mohamed Y. A. Bakhet¹  Fadlallah Mustafa Mosa²  Abdelmajid Ali Dafallah³  Eshag Mohamed Ahmed⁴ 

[1] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China.;

[2] Department of Mathematics and physics, Faculty of Education, University of Kassala, Kassala, Sudan.;

[3] Faculty of Petroleum and Hydrology Engineering, Peace University, Almugled, West Kordofan, Sudan.;

[4] Faculty of Pure and Applied Sciences, International University of Africa, Khartoum, Sudan.;

关键词: semilinear reaction-diffusion equation;    random dynamical system;    distribution derivatives;    measures of noncompactness.;   

DOI  :  10.30538/oms2020.0102

来源: DOAJ

【 摘 要 】

In this paper, we investigate the existence of random attractors for a semilinear reaction-diffusion equation with a nonlinearity having a polynomial growth of arbitrary order \(p-1(p\geq 2)\), and with distribution derivatives and multiplicative noise defined on unbounded domains. The random attractors are obtained in \(L^{2}(\mathbb{R}^{n})\) and \(L^{p}(\mathbb{R}^{n})\) respectively. The semilinear reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform a priori estimates for far-field values of solutions as well as the cut-off technique.

【 授权许可】

Unknown