This paper investigates the existence and uniform decay of global solutions to the initial and boundary value problem with clamped boundary conditions for a nonlinear beam equation with a strong damping.
In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infi...In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infinity.Within the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed estimates.The results obtained essentially improve and complete some previous works.展开更多
For β∈ R,the authors consider the evolution system in the unknown variables u and ααttu+αxxxxu+αxxtα-(β+αxu L22)αxxu=f,αttα-αxxα-αxxtα-αxxtu=0 describing the dynamics of type III thermoelastic extensi...For β∈ R,the authors consider the evolution system in the unknown variables u and ααttu+αxxxxu+αxxtα-(β+αxu L22)αxxu=f,αttα-αxxα-αxxtα-αxxtu=0 describing the dynamics of type III thermoelastic extensible beams,where the dissipation is entirely contributed by the second equation ruling the evolution of the thermal displacement α.Under natural boundary conditions,the existence of the global attractor of optimal regularity for the related dynamical system acting on the phase space of weak energy solutions is established.展开更多
In this paper, we study stochastic nonlinear beam equations with Levy jump, and use Lyapunov functions to prove existence of global mild solutions and asymptotic stability of the zero solution.
基金Supported by the NNSF of china(11271066,11326158)Supported by the grant of Shanghai Education Commission(13ZZ048)Supported by the Doctoral Innovational Fund of Donghua University(BC201138)
文摘This paper investigates the existence and uniform decay of global solutions to the initial and boundary value problem with clamped boundary conditions for a nonlinear beam equation with a strong damping.
基金National Natural Science Foundation of China(Grant Nos.12101265,12026431,11701230,11731005)Qing Lan Project of Jiangsu Province+1 种基金the dual creative(innovative and entrepreneurial)talents project in Jiangsu Province(Grant No.JSSCBS20210973)China Postdoctoral Science Foundation(Grant No.2022M721392)。
文摘In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infinity.Within the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed estimates.The results obtained essentially improve and complete some previous works.
基金supported by the Spanish Ministry of Science and Technology through the Project "Partial Defferential Equations in Thermomechanics.Theory and Applications"(No. MTM2009-08150)
文摘For β∈ R,the authors consider the evolution system in the unknown variables u and ααttu+αxxxxu+αxxtα-(β+αxu L22)αxxu=f,αttα-αxxα-αxxtα-αxxtu=0 describing the dynamics of type III thermoelastic extensible beams,where the dissipation is entirely contributed by the second equation ruling the evolution of the thermal displacement α.Under natural boundary conditions,the existence of the global attractor of optimal regularity for the related dynamical system acting on the phase space of weak energy solutions is established.
基金The Graduate Innovation Fund(20101049)of Jilin University
文摘In this paper, we study stochastic nonlinear beam equations with Levy jump, and use Lyapunov functions to prove existence of global mild solutions and asymptotic stability of the zero solution.
