共查询到20条相似文献,搜索用时 15 毫秒
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Amin Boumenir 《Mathematical Methods in the Applied Sciences》2019,42(15):5052-5059
We are concerned with the reconstruction of series solutions of a semilinear wave equation with a quadratic nonlinearity. The solution which may blow up in finite time is sought as a sum of exponential functions and is shown to be a classical one. The constructed solutions can be used to benchmark numerical methods used to approximate solutions of nonlinear equations. 相似文献
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Hansjörg Kielhöfer 《Journal of Mathematical Analysis and Applications》1979,68(2):408-420
Bifurcation of time periodic solutions and their regularity are proved for a semilinear wave equation, utt?uxx?λu=f(λ,x,u),x?(0,π), t?R, together with Dirichlet or Neumann boundary conditions at x = 0 and x = π. The set of values of the real parameter λ where bifurcation from the trivial solution u = 0 occurs is dense in . 相似文献
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We prove existence, uniqueness and regularity results for the global solutions of the semilinear wave equations. In particular,
we show existence of regular self-similar solutions. Also, we build some finite-energy asymptotically self-similar solutions.
Received: 20 September 1999; in final form: 10 May 2000 / Published online: 25 June 2001 相似文献
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P. Jameson Graber 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3137-3148
We consider a wave equation with semilinear porous acoustic boundary conditions. This is a coupled system of second and first order in time partial differential equations, with possibly semilinear boundary conditions on the interface. The results obtained are (i) strong stability for the linear model, (ii) exponential decay rates for the energy of the linear model, and (iii) local exponential decay rates for the energy of the semilinear model. This work builds on a previous result showing generation of a well-posed dynamical system. The main tools used in the proofs are (i) the Stability Theorem of Arendt-Batty, (ii) energy methods used in the study of a wave equation with boundary damping, and (iii) an abstract result of I. Lasiecka applicable to hyperbolic-like systems with nonlinearly perturbed boundary conditions. 相似文献
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Abbes Benaissa Salim A. Messaoudi 《NoDEA : Nonlinear Differential Equations and Applications》2006,12(4):391-399
The issue of stablity of solutions to nonlinear wave equations has been addressed by many authors. So many results concerning
energy decay have been established. Here in this paper we consider the following nonlinearly damped wave equation
a, b > 0, in a bounded domain and show that, for suitably chosen initial data, the energy of the solution decays exponentially
even if m > 2. 相似文献
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Piotr Biler 《Mathematical Methods in the Applied Sciences》1991,14(6):427-443
We study the asymptotic behaviour in time of the solutions of dissipative perturbations of wave-type equations in ?N, utt + But + Au + G(u) = 0, with commuting positive operators A, B and a power like non-linearity G(u). First we give some (pseudo) conformal invariants of the linear operator in the equation. This allows us to derive optimal decay rates for the solutions of the linearized problems. We then prove some decay estimates for the non-linear problems using the tools of scattering theory and the aforementioned conformal invariants. 相似文献
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We consider the semilinear parabolic equation ut=Δu+up on RN, where the power nonlinearity is subcritical. We first address the question of existence of entire solutions, that is, solutions defined for all x∈RN and t∈R. Our main result asserts that there are no positive radially symmetric bounded entire solutions. Then we consider radial solutions of the Cauchy problem. We show that if such a solution is global, that is, defined for all t?0, then it necessarily converges to 0, as t→∞, uniformly with respect to x∈RN. 相似文献
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Ahmed Bchatnia 《Applied Mathematics Letters》2010,23(8):935-939
In this note, we prove the global well posedness and the local energy decay for semilinear wave equation with small data. 相似文献
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We consider attractors Aη, η∈[0,1], corresponding to a singularly perturbed damped wave equation
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Science China Mathematics - We consider the periodic solutions of a semilinear variable coefficient wave equation arising from the forced vibrations of a nonhomogeneous string and the propagation... 相似文献
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Karen Yagdjian 《Journal of Mathematical Analysis and Applications》2007,336(2):1259-1286
We investigate the issue of existence of the self-similar solutions of the generalized Tricomi equation in the half-space where the equation is hyperbolic. We look for the self-similar solutions via the Cauchy problem. An integral transformation suggested in [K. Yagdjian, A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain, J. Differential Equations 206 (2004) 227-252] is used to represent solutions of the Cauchy problem for the linear Tricomi-type equation in terms of fundamental solutions of the classical wave equation. This representation allows us to prove decay estimates for the linear Tricomi-type equation with a source term. Obtained in [K. Yagdjian, The self-similar solutions of the Tricomi-type equations, Z. Angew. Math. Phys., in press, doi:10.1007/s00033-006-5099-2] estimates for the self-similar solutions of the linear Tricomi-type equation are the key tools to prove existence of the self-similar solutions. 相似文献
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A semilinear elliptic equation is considered in a domain with smooth boundary. The authors prove the existence and uniqueness
of positive solutions of different types, singular at an inner point, subject to the Dirichlet boundary conditions. Bibliography:
13 titles.
Translated from Trudy Seminara imeni I., G. Petrovskogo. No. 18, pp. 157–169, 1995. 相似文献