带有非线性有色噪声的p-Laplacian方程的随机吸引子  

Random Attractors of p-Laplacian Equation Driven by Nonlinear Colored Noise

作　　者：俞智慧[1] 李富智 YU Zhi-hui;LI Fu-zhi(School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China)

机构地区：[1]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《数学的实践与认识》2023年第8期248-253,共6页Mathematics in Practice and Theory

基　　金：江西省教育厅科学技术项目(GJJ2201803);江西省基础教育研究项目(SZUSYSX2021-998);江西省高等学校省级教学研究项目(JXJG-22-16-11);江西省自然科学基金(20224BAB201009)。

摘　　要：研究了带有非线性有色噪声的非自治p-Laplacian方程在有界域上的渐近行为.假设方程中非线性项的第三个分量具有任意阶的多项式增长指数,首先得到了方程解的一致估计以及解在L^(2)(O)中的拉回渐近紧性.最后得出了该方程生成的非自治随机动力系统存在唯一的拉回随机吸引子.This paper studies the asymptotic behavior of the non-autonomous p-Laplacian equation driven by nonlinear colored noise on the bounded domain.Assuming that the third component of the nonlinear term in the equation has a polynomial growth exponent of arbitrary order,we first obtain some uniform estimates of the solution and the pullback asymptotic compactness of the solution in L^(2)(O).Finally,a unique pullback random attractor of non-autonomous stochastic dynamic system generated by this equation is obtained.

关 键 词：P-LAPLACIAN方程 拉回随机吸引子 非线性 有色噪声 

分 类 号：O175[理学—数学]