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The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded [PDF]
Fundamental ResearchAlinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time solutions, provided that the initial data are compactly supported and ...
Shijie Dong +2 more
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Boundary Value Problems, 2011 In this paper, we consider the system of nonlinear viscoelastic equations u t t - Δ u + ∫ 0 t g 1 ( t - τ ) Δ u ( τ ) d τ - Δ u t = f 1 ( u , v ) , ( x , t )
Liang Fei, Gao Hongjun
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The Cauchy problem for the Klein–Gordon equation under the quartic potential in the de Sitter spacetime [PDF]
Journal of Mathematics and Physics, 2020 The Cauchy problem for the Klein-Gordon equation under the quartic potential is considered in the de Sitter spacetime. The existence of the global solution is shown based on the mechanism of the spontaneous symmetry breaking for the small positive Hubble
Makoto Nakamura
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Polynomial stability of the wave equation with distributed delay term on the dynamical control
Nonautonomous Dynamical Systems, 2021 Using the frequency domain approach, we prove the rational stability for a wave equation with distributed delay on the dynamical control, after establishing the strong stability and the lack of uniform stability.
Silga Roland, Bayili Gilbert
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Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes
Numerical Mathematics: Theory, Methods and Applications, 2022 In this paper, we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Padé Via Lanczos (PVL) method.
Shuyang Dai +4 more
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Stability estimate for the semi-discrete linearized Benjamin-Bona-Mahony equation
, 2021 In this work we study the semi-discrete linearized Benjamin-Bona-Mahony equation (BBM) which is a model for propagation of one-dimensional, unidirectional, small amplitude long waves in non-linear dispersive media.
R. Lecaros +2 more
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Quasi-stability and continuity of attractors for nonlinear system of wave equations
Nonautonomous Dynamical Systems, 2021 In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces.
Freitas M. M. +4 more
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Advances in Nonlinear Analysis, 2023 We are concerned with the stabilization of the wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic and frictional effects.
Jin Kun-Peng, Wang Li
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On a strongly damped semilinear wave equation with time-varying source and singular dissipation
Advances in Nonlinear Analysis, 2022 This paper deals with the global well-posedness and blow-up phenomena for a strongly damped semilinear wave equation with time-varying source and singular dissipative terms under the null Dirichlet boundary condition.
Yang Yi, Fang Zhong Bo
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Advanced Nonlinear Studies, 2022 The Chaplygin gas model is both interesting and important in the theory of gas dynamics and conservation laws, all the characteristic families of which are linearly degenerate. Majda conjectured that the shock formation never happens for smooth data.
Wei Dongyi, Zhang Zhifei, Zhao Wenbin
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