This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the...This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then prove the existence and uniqueness of tempered pullback random attractors for the random dynamical system generated by the solutions of considered equations in an appropriate Hilbert space. The proof is based on the uniform estimates and the decomposition of dynamical system.展开更多
The lump solutions and interaction solutions are mainly investigated for the(2+1)-dimensional KPI equation.According to relations of the undetermined parameters of the test functions,the N-soliton solutions are showed...The lump solutions and interaction solutions are mainly investigated for the(2+1)-dimensional KPI equation.According to relations of the undetermined parameters of the test functions,the N-soliton solutions are showed by computations of the Maple using the Hirota bilinear form for(2+1)-dimensional KPI equation.One type of the lump solutions for(2+1)-dimensional KPI equation has been deduced by the limit method of the N-soliton solutions.In addition,the interaction solutions between the lump and N-soliton solutions of it are studied by the undetermined interaction functions.The sufficient conditions for the existence of the interaction solutions are obtained.Furthermore,the new breather solutions for the(2+1)-dimensional KPI equation are considered by the homoclinic test method via new test functions including more parameters than common test functions.展开更多
The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^...The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^(n))and attracts all tempered random sets of L^(2)(R^(n))×L^(2)(R^(n))in the topology of Hs(R^(n))×L^(2)(R^(n))with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results.展开更多
文摘This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then prove the existence and uniqueness of tempered pullback random attractors for the random dynamical system generated by the solutions of considered equations in an appropriate Hilbert space. The proof is based on the uniform estimates and the decomposition of dynamical system.
基金Thisworkwas supportedby the National Natural Science Foundation of China(Grant Nos.11861013,11771444)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(No.201806)Promotion of the Basic Capacity of Middle and Young Teachers in Guangxi Universities(No.2017KY0340).
文摘The lump solutions and interaction solutions are mainly investigated for the(2+1)-dimensional KPI equation.According to relations of the undetermined parameters of the test functions,the N-soliton solutions are showed by computations of the Maple using the Hirota bilinear form for(2+1)-dimensional KPI equation.One type of the lump solutions for(2+1)-dimensional KPI equation has been deduced by the limit method of the N-soliton solutions.In addition,the interaction solutions between the lump and N-soliton solutions of it are studied by the undetermined interaction functions.The sufficient conditions for the existence of the interaction solutions are obtained.Furthermore,the new breather solutions for the(2+1)-dimensional KPI equation are considered by the homoclinic test method via new test functions including more parameters than common test functions.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.11771444,11871138)the Yue Qi Young Scholar Project+3 种基金China University of Mining and Technology(Beijing),China Scholarship Council(CSC)the Funding of V.C.&V.R.Key Lab of Sichuan Provincethe Funding of Young Backbone Teacher in Henan ProvinceHenan Overseas Expertise Introduction Center for Discipline Innovation.
文摘The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^(n))and attracts all tempered random sets of L^(2)(R^(n))×L^(2)(R^(n))in the topology of Hs(R^(n))×L^(2)(R^(n))with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results.
