共查询到20条相似文献,搜索用时 31 毫秒
1.
Min Ming Tang 《Journal of Mathematical Analysis and Applications》1977,57(2):368-381
In this paper we study the behavior of solutions of some quasilinear parabolic equations of the form as t → ∞. In particular, the solutions of these equations will decay to zero as t → ∞ in the L∞ norm. 相似文献
2.
Elliptic boundary value problems for systems of nonlinear partial differential equations of the form , i = 1(1)N, j, k = 1(1)n, pi ? 0, ? being a small parameter, with Dirichlet boundary conditions are considered. It is supposed that a formal approximation Z is given which satisfies the boundary conditions and the differential equations upto the order χ(?) = o(1) in some norm. Then, using the theory of differential inequalities, it is shown that under certain conditions the difference between the exact solution u of the boundary value problem and the formal approximation Z, taken in the sense of a suitable norm, can be made small. 相似文献
3.
Douglas Hensley 《Journal of Number Theory》1984,18(2):206-212
For a > 0 let , the sum taken over all n, 1 ≤ n ≤ x such that if p is prime and p|n then a < p ≤ y. It is shown for u < about () that , where pa(u) solves a delay differential equation much like that for the Dickman function p(u), and the asymptotic behavior of pa(u) is worked out. 相似文献
4.
Karen A Ames 《Journal of Mathematical Analysis and Applications》1984,103(1):172-183
Solutions of Cauchy problems for the singular equations (in a Hilbert space setting) and , ω={(x1,…,xM)εm: 0 < xi < ci for each i=1,…,m} are shown to be unique and to depend Hölder continuously on the initial data in suitably chosen measures for 0?t < T < ∞. Logarithmic convexity arguments are used to derive the inequalities from which such results can be deduced. 相似文献
5.
Wei-Ming Ni 《Journal of Differential Equations》1983,50(2):289-304
In this paper, we consider the uniqueness of radial solutions of the nonlinear Dirichlet problem satisfies some appropriate conditions and Ω is a bounded smooth domain in n which possesses radial symmetry. Our uniqueness results apply to, for instance, , or more generally λu + ∑i = 1kaiupi, λ ? 0, ai > 0 and pi > 1 with appropriate upper bounds, and Ω a ball or an annulus. 相似文献
6.
7.
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
8.
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
9.
10.
In a recent paper [3] the authors derived maximum principles which involved , where u(x) is a classical solution of an alliptic differential equation of the form (. In this paper these results are extended to the more general case in which is replaced by h(u, q2). 相似文献
11.
Elliott H Lieb 《Journal of Functional Analysis》1983,51(2):159-165
Let ψ1, …,ψN be orthonormal functions in d and let , or , and let . Lp bounds are proved for p, an example being , with p = d(d ? 2)?1. The unusual feature of these bounds is that the orthogonality of the ψi, yields a factor instead of N, as would be the case without orthogonality. These bounds prove some conjectures of Battle and Federbush (a Phase Cell Cluster Expansion for Euclidean Field Theories, I, 1982, preprint) and of Conlon (Comm. Math. Phys., in press). 相似文献
12.
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
13.
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
14.
David A Senechalle 《Journal of Functional Analysis》1978,27(2):203-214
Let L be a finite-dimensional normed linear space and let M be a compact subset of L lying on one side of a hyperplane through 0. A measure of flatness for M is the number , where the infimum is over all f in which are positive on M. Thus D(M) = 1 if M is flat, but otherwise D(M) > 1. On the other hand, let E(M) be a second measure on M defined as follows: If M is linearly independent, E(M) = 1. If M is linearly dependent, then (1) let Z be a minimal, linearly dependent subset of M; (2) partition Z into mutually exclusive subsets U = {u1, …, up} and V = {v1, …, vq} such that there exist positive coefficients ai and bi for which Σi = 1paiui = Σi = 1qbivi; (3) let ; (4) let E(M) be the supremum of all ratios r which can be formed by steps (1), (2) and (3). The main result of this paper is that these two measures are the same: D(M) = E(M). This result is then used to obtain results concerning the Banach distance-coefficient between an arbitrary finite-dimensional normed linear space and Hilbert space. 相似文献
15.
Richard E. Ewing 《Journal of Mathematical Analysis and Applications》1979,71(1):167-186
Numerical approximation of the solution of the Cauchy problem for the linear parabolic partial differential equation is considered. The problem: (p(x)ux)x ? q(x)u = p(x)ut, 0 < x < 1,0 < t? T; ; ; p(0) ux(0, t) = g(t), 0 < t0 ? t ? T, is ill-posed in the sense of Hadamard. Complex variable and Dirichlet series techniques are used to establish Hölder continuous dependence of the solution upon the data under the additional assumption of a known uniform bound for ¦ u(x, t)¦ when 0 ? x ? 1 and 0 ? t ? T. Numerical results are obtained for the problem where the data ?1, ?2 and g are known only approximately. 相似文献
16.
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
17.
Milton Rosenberg 《Journal of multivariate analysis》1978,8(2):295-316
Let p, q be arbitrary parameter sets, and let be a Hilbert space. We say that x = (xi)i?q, xi ? , is a bounded operator-forming vector (?Fq) if the Gram matrix 〈x, x〉 = [(xi, xj)]i?q,j?q is the matrix of a bounded (necessarily ≥ 0) operator on , the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from to . Then exists a linear operator ǎ from (the Banach space) Fq to Fp on (A) = {x:x ? Fq, is p × q bounded on } such that y = ǎx satisfies yj?σ(x) = {space spanned by the xi}, 〈y, x〉 = A〈x, x〉 and . This is a generalization of our earlier [J. Multivariate Anal.4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes. 相似文献
18.
Jan C Willems 《Journal of Differential Equations》1980,35(3):306-318
In this paper it is shown that the linear systems Σi defined by , are topologically equivalent if and only if they have the same Kronecker indices and the flows defined by considering trajectories modulo their controllable subspace are topologically equivalent. From some recent work of N. H. Kuiper (in “Manifolds—Tokyo 1973,” Univ. of Tokyo Press, Tokyo 1975) it is known exactly what this last condition amounts to. With these results at hand it is then not difficult to investigate the structural stability of and, in fact, structural stability turns out to be generic. 相似文献
19.
This paper presents a demonstrably convergent method of feasible directions for solving the problem min{φ(ξ)| gi(ξ)?0i=1,2,…,m}, which approximates, adaptively, both φ(x) and ▽φ(x). These approximations are necessitated by the fact that in certain problems, such as when , a precise evaluation of φ(x) and ▽φ(x) is extremely costly. The adaptive procedure progressively refines the precision of the approximations as an optimum is approached and as a result should be much more efficient than fixed precision algorithms.It is outlined how this new algorithm can be used for solving problems of the form under the assumption that Ωmξ={x|gi(x)?0, j=1,…,s} ∩n, Ωy={y|ζi(y)?0, i-1,…,t} ∩ m, with f, gj, ζi continuously differentiable, f(x, ·) concave, ζi convex for compact. 相似文献
20.
In connection with an optimization problem, all functions ?: In → with continuous nonzero partial derivatives and satisfying for all xi, xj ≠ I, i, j = 1,2,…, n (n > 2) are determined (I is an interval of positive real numbers). 相似文献