The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
该文主要考虑一类在R^(3)上带有Kirchhoff型非局部项的非线性椭圆方程−(a+b∫_(R)^(3)|∇u|^(2))Δu+V(x)u=Q(x)|u|^(p−1)u,x∈R^(3),(0.1)其中a,b>0是常数,p∈(1,5),V(x)和Q(x)均为L^(∞)(R^(3))函数.由于非局部项的出现,若按经典的...该文主要考虑一类在R^(3)上带有Kirchhoff型非局部项的非线性椭圆方程−(a+b∫_(R)^(3)|∇u|^(2))Δu+V(x)u=Q(x)|u|^(p−1)u,x∈R^(3),(0.1)其中a,b>0是常数,p∈(1,5),V(x)和Q(x)均为L^(∞)(R^(3))函数.由于非局部项的出现,若按经典的思路来应用山路引理得到这类方程的解(即山路解),必须要求3≤p<5.当p∈(1,3)时,应用山路引理的困难在于无法验证(PS)序列的有界性.为克服该困难,文献[Acta Math Sci,2025,45B(2):385-400]通过引入新的技巧证明了方程(0.1)在Q(x)≡1时对p∈(1,5)有山路解,并讨论了山路解与基态解的关系.该文拟在克服V(x)和Q(x)的相互影响下,将文献[Acta Math Sci,2025,45B(2):385-400]中的结果推广到Q(x)■1的一般情形.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
文摘该文主要考虑一类在R^(3)上带有Kirchhoff型非局部项的非线性椭圆方程−(a+b∫_(R)^(3)|∇u|^(2))Δu+V(x)u=Q(x)|u|^(p−1)u,x∈R^(3),(0.1)其中a,b>0是常数,p∈(1,5),V(x)和Q(x)均为L^(∞)(R^(3))函数.由于非局部项的出现,若按经典的思路来应用山路引理得到这类方程的解(即山路解),必须要求3≤p<5.当p∈(1,3)时,应用山路引理的困难在于无法验证(PS)序列的有界性.为克服该困难,文献[Acta Math Sci,2025,45B(2):385-400]通过引入新的技巧证明了方程(0.1)在Q(x)≡1时对p∈(1,5)有山路解,并讨论了山路解与基态解的关系.该文拟在克服V(x)和Q(x)的相互影响下,将文献[Acta Math Sci,2025,45B(2):385-400]中的结果推广到Q(x)■1的一般情形.
