共查询到20条相似文献,搜索用时 328 毫秒
1.
Yang Zhijian 《Mathematical Methods in the Applied Sciences》2009,32(9):1082-1104
The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in elasto‐plastic flow utt?div{|?u|m?1?u}?λΔut+Δ2u+g(u)=f(x). It proves that under rather mild conditions, the dynamical system associated with above‐mentioned IBVP possesses a global attractor, which is connected and has finite Hausdorff and fractal dimension in the phase spaces X1=H(Ω) × L2(Ω) and X=(H3(Ω)∩H(Ω)) × H(Ω), respectively. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
2.
A. Kh. Khanmamedov 《Mathematical Methods in the Applied Sciences》2010,33(2):177-187
In this paper the long‐time behaviour of the solutions of 2‐D wave equation with a damping coefficient depending on the displacement is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H(Ω) × L2(Ω) and H2(Ω)∩H(Ω) × H(Ω). Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
3.
Nguyen Thanh Long Pham Ngoc Dinh Alain 《Mathematical Methods in the Applied Sciences》1993,16(4):281-295
We study the following initial and boundary value problem: In section 1, with u0 in L2(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L2(0, T; H ∩ H2) ∩ L∞(0, T; H) if we assume u0 in H and f in C1(?,?). Numerical results are given for these two cases. 相似文献
4.
We consider a domain Ω in ?n of the form Ω = ?l × Ω′ with bounded Ω′ ? ?n?l. In Ω we study the Dirichlet initial and boundary value problem for the equation ? u + [(? ? ?… ? ?)m + (? ? ?… ? ?)m]u = fe?iωt. We show that resonances can occur if 2m ≥ l. In particular, the amplitude of u may increase like tα (α rational, 0<α<1) or like in t as t∞∞. Furthermore, we prove that the limiting amplitude principle holds in the remaining cases. 相似文献
5.
In this paper, some sufficient conditions under which the quasilinear elliptic system ‐div(∣?u∣p‐2?u) = uv, ‐div(∣?u∣q‐2?u) = uv in ?N(N≥3) has no radially symmetric positive solution is derived. Then by using this non‐existence result, blow‐up estimates for a class of quasilinear reaction–diffusion systems ut = div (∣?u∣p‐2?u)+uv,vt = div(∣?v∣q‐2?v) +uv with the homogeneous Dirichlet boundary value conditions are obtained. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
6.
For the Radon transform of functions with circular symmetry an inversion formula is proved in a new and elementary way. The inversion formula combined with Fourier theory is applied to Sommer-feld's integral for H, yielding a representation of products which generalizes Nicholson's integral for |H| 2. 相似文献
7.
Jean-Pierre Lohac 《Mathematical Methods in the Applied Sciences》1991,14(3):155-175
Consider the advection–diffusion equation: u1 + aux1 ? vδu = 0 in ?n × ?+ with initial data u0; the Support of u0 is contained in ?(x1 < 0) and a: ?n → ? is positive. In order to approximate the full space solution by the solution of a problem in ? × ?+, we propose the artificial boundary condition: u1 + aux1 = 0 on ∑. We study this by means of a transmission problem: the error is an O(v2) for small values of the viscosity v. 相似文献
8.
Nicola Visciglia 《Mathematical Methods in the Applied Sciences》2004,27(18):2153-2170
We consider the following semilinear wave equation: (1) for (t,x) ∈ ?t × ?. We prove that if the potential V(t,x) is a measurable function that satisfies the following decay assumption: ∣V(t,x)∣?C(1+t)(1+∣x∣) for a.e. (t,x) ∈ ?t × ? where C, σ0>0 are real constants, then for any real number λ that satisfies there exists a real number ρ(f,g,λ)>0 such that the equation has a global solution provided that 0<ρ?ρ(f,g,λ). Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Wojciech M. Zaja̧czkowski 《Mathematical Methods in the Applied Sciences》2011,34(5):544-562
We consider an initial‐boundary value problem for nonstationary Stokes system in a bounded domain Omega??3 with slip boundary conditions. We assume that Ω is crossed by an axis L. Let us introduce the following weighted Sobolev spaces with finite norms: and where ?(x) = dist{x, L}. We proved the result. Given the external force f∈L2, ?µ(ΩT), initial velocity v0∈H(Ω), µ∈?+\? there exist velocity v∈H(ΩT) and the pressure p, ?p∈L2, ?µ(ΩT) and a constant c, independent of v, p, f, such that As we consider the Stokes system in weighted Sobolev spaces the following two things must be used:
- 1. the slip boundary condition and
- 2. the Helmholtz–Weyl decomposition.
10.
We consider a second‐order differential operator A( x )=?∑?iaij( x )?j+ ∑?j(bj( x )·)+c( x ) on ?d, on a bounded domain D with Dirichlet boundary conditions on ?D, under mild assumptions on the coefficients of the diffusion tensor aij. The object is to construct monotone numerical schemes to approximate the solution of the problem A( x )u( x )=µ( x ), x ∈D, where µ is a positive Radon measure. We start by briefly mentioning questions of existence and uniqueness introducing function spaces needed to prove convergence results. Then, we define non‐standard stencils on grid‐knots that lead to extended discretization schemes by matrices possessing compartmental structure. We proceed to discretization of elliptic operators, starting with constant diffusion tensor and ending with operators in divergence form. Finally, we discuss W‐convergence in detail, and mention convergence in C and L1 spaces. We conclude by a numerical example illustrating the schemes and convergence results. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
11.
In this paper, we study the blow‐up behaviors for the solutions of parabolic systems ut=Δu+δ1e, vt=Δv+µ1u in ?×(0, T) with nonlinear boundary conditions Here δi?0, µj?0, pi?0, qj?0 and at least one of δiµjpiqj>0(i, j=1, 2). We prove that the solutions will blow up in finite time for suitable ‘large’ initial values. The exact blow‐up rates are also obtained. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
12.
In this paper the degenerate parabolic system ut=u(uxx+av). vt=v(vxx+bu) with Dirichlet boundary condition is studied. For , the global existence and the asymptotic behaviour (α1=α2) of solution are analysed. For , the blow‐up time, blow‐up rate and blow‐up set of blow‐up solution are estimated and the asymptotic behaviour of solution near the blow‐up time is discussed by using the ‘energy’ method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
13.
Yuka Naito 《Mathematical Methods in the Applied Sciences》2009,32(13):1609-1637
This paper is concerned with the thermoelastic plate equations in a domain Ω: subject to the boundary condition: u|=Dνu|=θ|=0 and initial condition: (u, ut, θ)|t=0=(u0, v0, θ0). Here, Ω is a bounded domain in ?n(n≧2). We assume that the boundary ?Ω of Ω is a C4 hypersurface. We obtain an Lp–Lq maximal regularity theorem. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
14.
We prove stability of the kink solution of the Cahn‐Hilliard equation ∂tu = ∂( ∂u − u/2 + u3/2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. We prove stability of the kink solution of the Cahn‐Hilliard equation ∂tu = ∂( ∂u − u/2 + u3/2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. © 1999 John Wiley & Sons, Inc. 相似文献
15.
Thomas Schott 《Mathematische Nachrichten》1998,196(1):231-250
This paper is a continuation of [8]. We study weighted function spaces of type B and F on the Euclidean space Rn, where u is a weight function of at most exponential growth. In particular, u(χ (±|χ|) is an admissible weight. We deal with atomic decompositions of these spaces. Furthermore, we prove that the spaces B and F are isomorphic to the corresponding unweighted spaces B and F. 相似文献
16.
This paper is devoted to the study of the Cauchy problem of incompressible magneto‐hydrodynamics system in the framework of Besov spaces. In the case of spatial dimension n?3, we establish the global well‐posedness of the Cauchy problem of an incompressible magneto‐hydrodynamics system for small data and the local one for large data in the Besov space ? (?n), 1?p<∞ and 1?r?∞. Meanwhile, we also prove the weak–strong uniqueness of solutions with data in ? (?n)∩L2(?n) for n/2p+2/r>1. In the case of n=2, we establish the global well‐posedness of solutions for large initial data in homogeneous Besov space ? (?2) for 2<p<∞ and 1?r<∞. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
Yinnian He Kaitai Li Chunshan Zhao 《Numerical Methods for Partial Differential Equations》2004,20(5):723-741
This article provides a stability analysis for the backward Euler schemes of time discretization applied to the spatially discrete spectral standard and nonlinear Galerkin approximations of the nonstationary Navier‐Stokes equations with some appropriate assumption of the data (λ, u0, f). If the backward Euler scheme with the semi‐implicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraint Δt ≤ (2/λλ1). Moreover, if the backward Euler scheme with the explicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraints Δt = O(λ) and Δt = O(λ), respectively, where λ ≤ λ, which shows that the restriction on the time step of the spectral nonlinear Galerkin method is less than that of the spectral standard Galerkin method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 相似文献
18.
Bio Soumarou Chabi Gado Marc Durand Cme Goudjo 《Mathematical Methods in the Applied Sciences》2004,27(10):1221-1239
Our problem is about propagation of waves in stratified strips. The operators are quite general, a typical example being a coupled elasto‐acoustic operator H defined in ?2 × I where I is a bounded interval of ? with coefficients depending only on z∈I. One applies the ‘conjugate operator method’ to an operator obtained by a spectral decomposition of the partial Fourier transform ? of H. Around each value of the spectrum (except the eigenvalues) including the thresholds, a conjugate operator may be constructed which ensures the ‘good properties’ of regularity for H. A limiting absorption principle is then obtained for a large class of operators at every point of the spectrum (except eigenvalues). If the point is a threshold, the limiting absorption principle is valid in a closed subspace of the usual one (namely L, with s>½) and we are interested by the behaviour of R(z), z close to a threshold, applying in the usual space L, with s>½ when z tends to the threshold. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
19.
Olaf Bhme 《Mathematische Nachrichten》1983,113(1):163-169
By using the LITTLEWOOD matrices A2n we generalize CLARKSON' S inequalities, or equivalently, we determine the norms ‖A2n: l(LP) → l(LP)‖ completely. The result is compared with the norms ‖A2n: l → l‖, which are calculated implicitly in PIETSCH [6]. 相似文献
20.
We consider the buckling problem for a family of thin plates with thickness parameter ε. This involves finding the least positive multiple λ of the load that makes the plate buckle, a value that can be expressed in terms of an eigenvalue problem involving a non‐compact operator. We show that under certain assumptions on the load, we have λ = ??(ε2). This guarantees that provided the plate is thin enough, this minimum value can be numerically approximated without the spectral pollution that is possible due to the presence of the non‐compact operator. We provide numerical computations illustrating some of our theoretical results. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献