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1.
《Applied Mathematics Letters》2001,14(2):253-260
We consider here solutions to a Kuramoto-Sivashinsky equation in space dimension two. It is shown that these solutions are analytic in time with values in a Gevrey class of functions. 相似文献
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Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions 总被引:1,自引:0,他引:1
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin–Voigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. 相似文献
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We consider a variable-coefficient wave equation with nonlinear damped acoustic boundary conditions. Well-posedness in the Hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups. 相似文献
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This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity in a bounded domain . We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique. 相似文献
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A weak formulation for the so-called semilinear strongly damped wave equation with constraint is introduced and a corresponding notion of solution is defined. The main idea consists in the use of duality techniques in Sobolev–Bochner spaces, aimed at providing a suitable “relaxation” of the constraint term. A global in time existence result is proved under the natural condition that the initial data have finite “physical” energy. 相似文献
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Ludmila S. Pulkina 《Proceedings of the Steklov Institute of Mathematics》2012,278(1):199-207
Two problems with nonlinear boundary conditions are studied. Existence and uniqueness theorems are proved for generalized solutions to each problem. 相似文献
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We study the initial boundary value problem for the nonlinear viscoelastic wave equation with strong damping term and dispersive term. By introducing a family of potential wells we not only obtain the invariant sets, but also prove the existence and nonexistence of global weak solution under some conditions with low initial energy. Furthermore, we establish a blow-up result for certain solutions with arbitrary positive initial energy (high energy case) 相似文献
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周盛凡 《应用数学学报(英文版)》2000,16(3):266-273
1. IntroductionConsider the strongly damped nonlinear wave equationwith the Dirichlet boundary conditionand the initial value conditionswhere u = u(x, t) is a real--valued function on fi x [0, co), fi is an open bounded set of R"with smooth boundary off, or > 0, g e L'(fl), D(--Q) ~ Ha(~~) n H'(fl).We assume for the function f(u) as follows'f(u) E CI (R, R) satisfiesfor any ig al, uZ E R, where k, hi > 0, i ~ 0, 1, 2, 61 > 0 and 0 5 6o < 1'The type of equation (1) can be regarded as the… 相似文献
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A mixed finite element Galerkin method is analyzed for a strongly damped wave equation. Optimal error estimates in L2‐norm for the velocity and stress are derived using usual energy argument, while those for displacement are based on the nonstandard energy formulation of Baker. Both a semi‐discrete scheme and a second‐order implicit‐time discretization method are discussed, and it is shown that the results are valid for all t > 0. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 105–119, 2001 相似文献
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一类强阻尼波方程解的存在性和爆破性 总被引:3,自引:0,他引:3
徐江 《高校应用数学学报(A辑)》2006,21(2):157-164
讨论一类强阻尼波方程解的局部存在性,并利用势井理论研究解的整体存在性和爆破性. 相似文献
13.
Yang Zhijian 《Mathematical Methods in the Applied Sciences》2003,26(12):1047-1066
The paper studies the existence, asymptotic behaviour and stability of global solutions to the initial boundary value problem for a class of strongly damped non‐linear wave equations. By a H00.5ptk‐Galerkin approximation scheme, it proves that the above‐mentioned problem admits a unique classical solution depending continuously on initial data and decaying to zero as t→+∞as long as the non‐linear terms are sufficiently smooth; they, as well as their derivatives or partial derivatives, are of polynomial growth order and the initial energy is properly small. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
14.
Tran Thanh Binh Nguyen Huu Can Danh Hua Quoc Nam Tran Ngoc Thach 《Mathematical Methods in the Applied Sciences》2020,43(7):4317-4335
In this paper, we consider an inverse problem for a strongly damped wave equation in two dimensional with statistical discrete data. Firstly, we give a representation for the solution and then present a discretization form of the Fourier coefficients. Secondly, we show that the solution does not depend continuously on the data by stating a concrete example, which makes the solution be not stable and thus the present problem is ill-posed in the sense of Hadamard. Next, we use the trigonometric least squares method associated with the Fourier truncation method to regularize the instable solution of the problem. Finally, the convergence rate of the error between the regularized solution and the sought solution is estimated and also investigated numerically. 相似文献
15.
Le Xuan Truong Le Thi Phuong Ngoc Alain Pham Ngoc Dinh Nguyen Thanh Long 《Nonlinear Analysis: Real World Applications》2010,11(3):1289-1303
This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated the boundary conditions of two-point type. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional. Finally, we present some numerical results. 相似文献
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This paper is concerned with the initial‐boundary value problem for one‐dimensional strongly damped wave equation involving p‐Laplacian. For p > 2 , we establish the existence of weak local attractors for this problem in . Under restriction 2 < p < 4, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in , and this attractor is a bounded subset of . Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
18.
In this paper, following the techniques of Foias and Temam, we establish suitable Gevrey class regularity of solutions to the supercritical quasi-geostrophic equations in the whole space, with initial data in “critical” Sobolev spaces. Moreover, the Gevrey class that we obtain is “near optimal” and as a corollary, we obtain temporal decay rates of higher order Sobolev norms of the solutions. Unlike the Navier–Stokes or the subcritical quasi-geostrophic equations, the low dissipation poses a difficulty in establishing Gevrey regularity. A new commutator estimate in Gevrey classes, involving the dyadic Littlewood–Paley operators, is established that allow us to exploit the cancellation properties of the equation and circumvent this difficulty. 相似文献
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Salah-Eddine Chorfi Ghita El Guermai Lahcen Maniar Walid Zouhair 《Mathematical Methods in the Applied Sciences》2023,46(1):911-929
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fréchet differentiability of the Tikhonov functional is studied, and a gradient formula is obtained via the solution of an associated adjoint problem. Then, the Lipschitz continuity of the gradient is proved. Furthermore, the existence and the uniqueness for the minimization problem are discussed. Finally, some numerical experiments for the reconstruction of an internal wave force are implemented via a conjugate gradient algorithm. 相似文献