摘要
研究一类Kirchhoff型分数阶随机反应扩散方程组初边值问题.由于存在分数阶微分算子和非线性随机项,这类问题的解相对复杂.首先把问题改写为Ito随机积分方程初值问题,其次对非线性项作合理假设,最后利用Galerkin方法证明了弱解的存在唯一性.证明的过程中利用了分数阶Sobolev空间的性质、分数阶Laplace算子的性质及极大增殖算子的Crandal-Liggett定理等相关结论.进一步,推广了文献的结论.
In this article,an initial boundary value problem for a class of Kirchhoff type fractional stochastic reaction-diffusion systems is studied.Due to the fractional differential operator and nonlinear stochastic term,the solutions to such problems are relatively difficult.The problem as an initial value problem for Ito stochastic integral equations is first rewritten,then reasonable assumptions on the nonlinear term is proposed,and finally the existence and uniqueness of weak solutions by Galerkin method is proved.In the proof,relevant conclusions such as the properties of fractional Sobolev spaces,the properties of fractional Laplacian,and the Crandal Leggett theorem of maximum multiplication operators were utilized.In addition,this article extends references[1]and[2].
作者
马佳欣
鄢立旭
Ma Jiaxin;Yan Lixu(Northeast Forestry University)
出处
《哈尔滨师范大学自然科学学报》
CAS
2023年第6期9-14,共6页
Natural Science Journal of Harbin Normal University
基金
中央高校项目(2572022BC06)
