共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
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
3.
4.
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
5.
Ethelbert N Chukwu 《Journal of Mathematical Analysis and Applications》1980,76(1):283-296
Sufficient conditions are developed for the null-controllability of the nonlinear delay process (1) when the values of the control functions u lie in an m-dimensional unit cube Cm of Em. Conditions are placed on f which guarantee that if the uncontrolled system is uniformly asymptotically stable and if the linear control system x(t) = L(t, xt) + B(t) u(t) is proper, then (1) is null-controllable. 相似文献
6.
J.G. Besjes 《Journal of Mathematical Analysis and Applications》1974,48(2):594-609
We consider the first initial-boundary value problem for and L1 are linear elliptic partial differential operators) and investigate the properties of u(x, t, ?) as ? ↓ 0 in the maximum norm. Special attention is paid to approximations obtained by the boundary layer method. We use a priori estimates. 相似文献
7.
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
8.
For parabolic initial boundary value problems various results such as , where u satisfies , are demonstrated via the maximum principle and potential theoretic estimates. 相似文献
9.
10.
M.G. Crandall S.-O. Londen J.A. Nohel 《Journal of Mathematical Analysis and Applications》1978,64(3):701-735
We study the nonlinear Volterra equation , (1) as well as the corresponding problem with infinite delay . (7) Under various assumptions on the nonlinear operators A, B and on the given functions a, F, f, h existence theorems are obtained for (1) and (7, followed by results concerning boundedness and asymptotic behaviour of solutions on (0 ? < ∞); two applications of the theory to problems of nonlinear heat flow with “infinite memory” are also discussed. 相似文献
11.
Let Ω be a simply connected domain in the complex plane, and , the space of functions which are defined and analytic on , if K is the operator on elements defined in terms of the kernels ki(t, s, a1, …, an) in by is the identity operator on , then the operator I ? K may be factored in the form (I ? K)(M ? W) = (I ? ΠK)(M ? ΠW). Here, W is an operator on defined in terms of a kernel w(t, s, a1, …, an) in by Wu = ∝antw(t, s, a1, …, an) u(s, a1, …, an) ds. ΠW is the operator; ΠWu = ∝an ? 1w(t, s, a1, …, an) u(s, a1, …, an) ds. ΠK is the operator; ΠKu = ∑i = 1n ? 1 ∝aitki(t, s, a1, …, an) ds + ∝an ? 1tkn(t, s, a1, …, an) u(s, a1, …, an) ds. The operator M is of the form m(t, a1, …, an)I, where and maps elements of into itself by multiplication. The function m is uniquely derived from K in the following manner. The operator K defines an operator on functions u in , by . A determinant of the operator is defined as an element of . This is mapped into by setting an + 1 = t to give m(t, a1, …, an). The operator I ? ΠK may be factored in similar fashion, giving rise to a chain factorization of I ? K. In some cases all the matrix kernels ki defining K are separable in the sense that ki(t, s, a1, …, an) = Pi(t, a1, …, an) Qi(s, a1, …, an), where Pi is a 1 × pi matrix and Qi is a pi × 1 matrix, each with elements in , explicit formulas are given for the kernels of the factors W. The various results are stated in a form allowing immediate extension to the vector-matrix case. 相似文献
12.
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
13.
Jorge L.C Sanz Thomas S Huang 《Journal of Mathematical Analysis and Applications》1984,104(1):302-308
In this paper, the problem of phase reconstruction from magnitude of multidimensional band-limited functions is considered. It is shown that any irreducible band-limited function f(z1…,zn), zi ? , i=1, …, n, is uniquely determined from the magnitude of f(x1…,xn): | f(x1…,xn)|, xi ? , i=1,…, n, except for (1) linear shifts: i(α1z1+…+αn2n+β), β, αi?, i=1,…, n; and (2) conjugation: . 相似文献
14.
A technique for the numerical approximation of matrix-valued Riemann product integrals is developed. For a ? x < y ? b, Im(x, y) denotes , and Am(x, y) denotes an approximation of Im(x, y) of the form , where ak and yik are fixed numbers for i = 1, 2,…, m and k = 1, 2,…, N and xik = x + (y ? x)yik. The following result is established. If p is a positive integer, F is a function from the real numbers to the set of w × w matrices with real elements and F(1) exists and is continuous on [a, b], then there exists a bounded interval function H such that, if n, r, and s are positive integers, , then Further, if F(j) exists and is continuous on [a, b] for j = 1, 2,…, p + 1 and A is exact for polynomials of degree less than p + 1 ? j for j = 1, 2,…, p, then the preceding result remains valid when Aj is substituted for Ij. 相似文献
15.
J.L. Brenner 《Journal of Mathematical Analysis and Applications》1985,106(2):427-442
Sharp inequalities are derived for certain (polynomial-like) functions of the real variables pi (i = 1(1)σ) by interpreting pi as the probabilities that various switches be thrown in certain directions. Parameters mv in the inequalities are at first taken to be integers; later the inequalities are established when mv are arbitrary real numbers. The side condition ∑pi = 1 occurs throughout analysis, so there are many corollaries. Examples of the inequalities established are valid ifm>1 valid if m > 1, n > r + 1, 0 < p, s, p + s ? 1, and also valid if . (1.03) 相似文献
16.
F.J. Massey 《Journal of Differential Equations》1976,22(2):416-427
Analyticity in t of solutions u(t) of nonlinear evolution equations of the form , is established under suitable conditions on . An application is given to quasilinear parabolic equations. 相似文献
17.
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
18.
A set {b1,b2,…,bi} ? {1,2,…,N} is said to be a difference intersector set if {a1,a2,…,as} ? {1,2,…,N}, j > ?N imply the solvability of the equation ax ? ay = b′; the notion of sum intersector set is defined similarly. The authors prove two general theorems saying that if a set {b1,b2,…,bi} is well distributed simultaneously among and within all residue classes of small moduli then it must be both difference and sum intersector set. They apply these theorems to investigate the solvability of the equations (, , , (where () denotes the Legendre symbol) and to show that “almost all” sets form both difference and sum intersector sets. 相似文献
19.
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
20.
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