无界区域上带有记忆项的反应扩散方程全局吸引子的存在性OA
Global attractor for the reaction-diffusion equation with memory in unbounded domain
证明具有记忆项的反应扩散方程ut-Δu+λu-∫∞0k(s)Δu(t-s)ds+f(u)=g,(x,t)∈Rn×R+,在无界区域中存在全局吸引子,其中,函数g∈H-1(Rn),函数f满足适当的增长性条件.使用非紧性测度方法,证明了该方程在空间L2(Rn)×L2μ(R+;H1(Rn))中存在全局吸引子.
The existence of a global attractor is given for the following reaction-diffusion equation with memory in an unbounded domain∞ut-Δu+λu-∫k(s)Δu(t-s)ds+f(u)=g,(x,t)∈Rn×R+,0 where g∈H-1(Rn)and the function f satisfies some suitable increasing conditions.By using the method of non-compactness measure,the existence of global attractors in L2(Rn)×L2μ(R+;H1(Rn))is established.
郑好;张晋
河海大学 数学学院,江苏 南京 210098河海大学 数学学院,江苏 南京 210098
全局吸引子记忆项反应扩散方程无界区域非紧性测度
global attractormemory termreaction-diffusion equationunbounded domainnon-compactness measure
《西北师范大学学报（自然科学版）》 2026 (1)
59-66,8
国家自然科学基金资助项目(11601117)国家留学基金资助项目(202106715004)
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