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作者:Sergo Kharibegashvili , Bidzina Midodashvili
来源:[J].Lithuanian Mathematical Journal(IF 0.346), 2017, Vol.57 (3), pp.331-350
摘要:We consider a nonlocal problem in time for semilinear multidimensional wave equations and prove theorems on existence, uniqueness, and nonexistence of solutions.
作者:Chenmin Sun , Nikolay Tzvetkov
来源:[J].Journal of Functional Analysis(IF 1.252), 2020, Vol.278 (2)
摘要:Abstract(#br)We consider fractional wave equations with exponential or arbitrary polynomial nonlinearities. We prove the global well-posedness on the support of the corresponding Gibbs measures. We provide ill-posedness constructions showing that the results are truly super-criti...
作者:Annegret Y. Burtscher , Roland Donninger
来源:[J].Communications in Mathematical Physics(IF 1.971), 2017, Vol.353 (2), pp.549-596
摘要:The focusing cubic wave equation in three spatial dimensions has the explicit solution \({\sqrt{2}/t}\) . We study the stability of the blowup described by this solution as \({t \to 0}\) without symmetry restrictions on the data. Via the conformal invariance of the equation we ob...
作者:Jianghao Hao , Haiying Wei
来源:[J].Boundary Value Problems(IF 0.922), 2017, Vol.2017 (1)
摘要:In this paper we consider a quasilinear viscoelastic wave equation with initial-boundary conditions, strong damping and source term. Under suitable assumptions on the initial data and the relaxation function, we establish a blow-up result of a solution for negative initial energy...
作者:Michael Ruzhansky , Niyaz Tokmagambetov
来源:[J].Archive for Rational Mechanics and Analysis(IF 2.292), 2017, Vol.226 (3), pp.1161-1207
摘要:Given a Hilbert space \({\mathcal{H}}\) , we investigate the well-posedness of the Cauchy problem for the wave equation for operators with a discrete non-negative spectrum acting on \({\mathcal{H}}\) . We consider the cases when the time-dependent propagation speed is regular, H...
作者:Antonín Slavík
来源:[J].Qualitative Theory of Dynamical Systems, 2017, Vol.16 (2), pp.299-315
摘要:We study the well-posedness of initial-value problems for systems of partial dynamic equations with discrete space and arbitrary time domain. We also present the superposition principle for infinite linear combinations of solutions. As an example, we consider the discrete-space wave equation...
作者:Alberto Bressan , Geng Chen
来源:[J].Archive for Rational Mechanics and Analysis(IF 2.292), 2017, Vol.226 (3), pp.1303-1343
摘要:The nonlinear wave equation \({u_{tt}-c(u)(c(u)u_x)_x=0}\) determines a flow of conservative solutions taking values in the space \({H^1(\mathbb{R})}\) . However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construc...
作者:Wei Han
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2017, Vol.456 (1), pp.525-542
摘要:Abstract(#br)This paper is devoted to prove the sharpness on the lower bound of the life-span of classical solutions to the initial-boundary value problem for one dimensional general quasilinear wave equations in the general case obtained in [10]. What's more, the originality of ...
作者:Qinghong Li , Yongzhong Song , Yushun Wang
来源:[J].Applied Mathematics and Computation(IF 1.349), 2005, Vol.177 (1), pp.36-43
摘要:Abstract(#br)Many conservative PDEs, such as various wave equations, Schrödinger equations, KdV equations and so on, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. In this note, we show the di...

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