共查询到20条相似文献,搜索用时 15 毫秒
1.
Philip Brenner 《Journal of Differential Equations》1985,56(3):310-344
Asymptotic properties of solutions of the nonlinear Klein-Gordon equation ?t2u ? Δu + m2u + f(u) = 0 (NLKG) , , are investigated, which are inherited from the corresponding solutions v of the (linear) Klein-Gordon equation ?t2v ? Δv + m2v = 0, , (KG) In particular, the finiteness of time-integrals in Lq over R+ of certain Sobolevnorms in space of the solution is proved to be such a hereditary property. Together with a device by W. A. Strauss and a weak decay result for the (KG) due to R. S. Strichartz, this is used to prove that under suitable restrictions on the nonlinearity, the scattering operator for the (NLKG) is defined on all of L21 × L2 for n = 3. 相似文献
2.
The large time behavior of zero-mass solutions to the Cauchy problem for the convection–diffusion equation is studied when q>1 and the initial datum u0 belongs to and satisfies . We provide conditions on the size and shape of the initial datum u0 as well as on the exponent q>1 such that the large time asymptotics of solutions is given either by the derivative of the Gauss–Weierstrass kernel, or by a self-similar solution of the equation, or by hyperbolic N-waves. To cite this article: S. Benachour et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
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4.
Sadanand Srivastava K.A. Zischka 《Journal of Mathematical Analysis and Applications》1974,45(3):764-776
The present work is intended to be a comprehensive and systematic treatment of the “radiation condition” (a particular case being Sommerfeld's radiation condition) which guarantees the uniqueness of the solution of the exterior boundary value problems for the second-order linear elliptic differential equation (which one can also consider as the reduced general wave equation) in n-dimensional Euclidean space En. First of all, Sobolev's integral formula is generalized. This is accomplished by means of the concept of retarded argument and auxiliary functions σn and τ (in an appendix). Furthermore, some additional restrictions are imposed on σn and τ. Second, using this generalized integral formula, conditions which are a generalization of the classical Sommerfeld's radiation condition are found. Then the maximum principle for the solution in an unbounded domain is stated which finally leads to the uniqueness theorem for the exterior boundary value problem. Special cases of (A) such as Δu + k2u = 0 and Δu + k2(x)u = 0 can also be deduced. 相似文献
5.
Beny Neta 《Journal of Mathematical Analysis and Applications》1982,89(2):598-611
Galerkin's method with appropriate discretization in time is considered for approximating the solution of the nonlinear integro-differential equation , 0 < x < 1, 0 < t < T.An error estimate in a suitable norm will be derived for the difference u ? uh between the exact solution u and the approximant uh. It turns out that the rate of convergence of uh to u as h → 0 is optimal. This result was confirmed by the numerical experiments. 相似文献
6.
The authors investigate the Tjon-Wu (TW) equation: (TW) , which has been obtained from a classical Boltzmann equation by applying the Abel transform. (TW) is considered as an ordinary differential equation first in the space L2={u:[0,∞)→R|∫x∞|u(x)|2exdx < + ∞}The authors establish existence and uniqueness of solutions in disks of codimension 2 around 0 and around e?x. Asymptotic stability of these latter functions is also established. The basic tool is an unusual eigenvalue property of the nonlinear right-hand side of (TW) which leads to a reformulation of (TW) as a differential equation in l2. Similar results are established in L1 working with (TW) directly. 相似文献
7.
In this Note we study the Schrödinger equation i?tu+Δu+V0u+V1u=0 on with initial condition , where V0 is a coulombian potential, singular at finite distance and V1 is an electric potential, possibly unbounded. Both of them may depend on space and time variables. We prove that this problem is well-posed and that the regularity of the initial data is conserved for the solution. The detailed proof will be given elsewhere (Baudouin et al., in press). To cite this article: L. Baudouin et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
8.
Rym Worms 《Comptes Rendus Mathematique》2002,334(8):709-712
We compare assumptions used in [4] in order to study the rate of convergence to 0, as u→s+(F), of , where is the survival function of the excesses over u, s+(F)=sup{x,F(x)<1} is the upper end point of the distribution function (d.f.) F and is the survival function of the Generalized Pareto Distribution, with assumptions used in [2] in order to study the rate of convergence to 0, as n→+∞, of , where Hγ is the d.f. of an extreme value distribution. In each case, an indicator linked to regular variation assumptions had been introduced. We characterize situations where these two indicators coincide, and others where they are different. To cite this article: R. Worms, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 709–712. 相似文献
9.
We construct two d-dimensional independent diffusions , with the same viscosity ν≠0 and the same drift u(x,t)=(pρta(x)v1+(1?p)ρtb(x)v2)/(pρta(x)+(1?p)ρtb(x)), where ρta,ρtb are respectively the density of Xta and Xtb. Here and p∈(0,1) are given. We show that is the unique weak solution of the following pressureless gas system such that as t→0+. To cite this article: A. Dermoune, S. Filali, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
10.
Yu.V. Egorov V.A. Galaktionov V.A. Kondratiev S.I. Pohozaev 《Comptes Rendus Mathematique》2002,335(10):805-810
We study the asymptotic behaviour of global bounded solutions of the Cauchy problem for the semilinear 2mth order parabolic equation ut=?(?Δ)mu+|u|p in RN×R+, where m>1, p>1, with bounded integrable initial data u0. We prove that in the supercritical Fujita range p>pF=1+2m/N any small global solution with nonnegative initial mass, , exhibits as t→∞ the asymptotic behaviour given by the fundamental solution of the linear parabolic operator (unlike the case where solutions can blow-up for any arbitrarily small initial data). A discrete spectrum of other possible asymptotic patterns and the corresponding monotone sequence of critical exponents , where p0=pF, are discussed. To cite this article: Yu.V. Egorov et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 805–810. 相似文献
11.
Louis B Bushard 《Journal of Differential Equations》1976,21(2):439-443
A comparison theorem and a uniqueness corollary for positive solutions to the equation on the closure of a bounded open set are found. The important hypotheses on the nonlinear coefficients are that each pi is positive and monotone increasing in u while q is monotone decreasing in u. An application is made to equations arising in the theory of chemical reactors. 相似文献
12.
In this Note we consider nonnegative solutions for the nonlinear equation in , where is the so called Pucci operator and the ei are the eigenvalues of M et Λ?λ>0. We prove that if u satisfies the decreasing estimate for some β satisfying (β?1)(p?1)>2+α then u is radial. In a second time we prove that if and u is a nonnegative radial solution of (1), u(x)=g(r), such that g″ changes sign at most once, then u is zero. To cite this article: I. Birindelli, F. Demengel, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
13.
In this paper we study the existence, uniqueness, and regularity of the solutions for the Cauchy problem for the evolution equation is in (0, 1), 0 ? t ? T, T is an arbitrary positive real number,f(s)?C1, and g(x, t)?L∞(0, T; L2(0, 1)). We prove the existence and uniqueness of the weak solutions for (1) using the Galerkin method and a compactness argument such as that of J. L. Lions. We obtain regular solutions using eigenfunctions of the one-dimensional Laplace operator as a basis in the Galerkin method. 相似文献
14.
Results on partition of energy and on energy decay are derived for solutions of the Cauchy problem . Here the Aj's are constant, k × k Hermitian matrices, x = (x1,…, xn), t represents time, and u = u(t, x) is a k-vector. It is shown that the energy of Mu approaches a limit , where M is an arbitrary matrix; that there exists a sufficiently large subspace of data ?, which is invariant under the solution group U0(t) and such that depending on ? and that the local energy of nonstatic solutions decays as . More refined results on energy decay are also given and the existence of wave operators is established, considering a perturbed equation at infinity. 相似文献
15.
We characterize the uniform algebras A on a compact Hausdorff space X which contain a sequence {uj}j = 0∞ of unimodular elements with and closed span in terms of the maximal ideal space of A. Roughly, the essential set of A looks like (at most) countably many copies of the boundary of the unit disk, and A looks like the disk algebra on each. 相似文献
16.
David W. Bange 《Journal of Differential Equations》1975,17(1):61-72
This paper treats the quasilinear, parabolic boundary value problem u(0, t) = ?1(t); u(l, t) = ?2(t) on an infinite strip with the functions being periodic in t. The major theorem of the paper gives sufficient conditions on for this problem to have a periodic solution u(x, t) which may be constructed by successive approximations with an integral operator. Some corollaries to this theorem offer more explicit conditions on and indicate a method for determining the initial estimate at which the iteration may begin. 相似文献
17.
Consider the nonlinear integro-differential equation , 0 < x <, 0 < t < T, with appropriate initial and boundary conditions. This problem serves as a model for one-dimensional heat flow in materials with memory. The numerical solution via finite elements was discussed in B. Neta [J. Math. Anal. Appl.89 (1982), 598–611]. In this paper we compare the results obtained there with finite difference approximation from the point of view of accuracy and computer storage. It turns out that the finite difference method yields comparable results for the same mesh spacing using less computer storage. 相似文献
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19.
Didier Robert 《Journal of Functional Analysis》1982,45(1):74-94
Let . Under suitable conditions we prove that is a pseudodifferential operator whose symbol has an asymptotic: . More general pseudodifferential operator's classes are also considered. We apply this result to study the semi-classical behaviour of the spectrum of Hv as h → 0. So, we improve recent results obtained by J. Chazarain and by the author in collaboration with B. Helffer. Furthermore we give a precise meaning to the formal development considered in B. Grammaticos and A. Voros' work (Ann. Physics123 (1979), 359–380). 相似文献