共查询到20条相似文献,搜索用时 15 毫秒
1.
Thomas G Kurtz 《Journal of Functional Analysis》1976,23(2):135-144
For each t ? 0, let A(t) generate a contraction semigroup on a Banach space L. Suppose the solution of ut = ?A(t)u is given by an evolution operator V?(t, s). Conditions are given under which converges strongly as ? → 0 to a semigroup T(t) generated by the closure of .This result is applied to the following situation: Let B generate a contraction group S(t) and the closure of ?A + B generate a contraction semigroup S?(t). Conditions are given under which converges strongly to a semigroup generated by the closure of . This work was motivated by and generalizes a result of Pinsky and Ellis for the linearized Boltzmann Equation. 相似文献
2.
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
3.
David Terman 《Journal of Differential Equations》1983,47(3):406-443
We consider the pure initial value problem for the system of equations , the initial data being (ν(x, 0), w(x, 0)) = (?(x), 0). Here , where H is the Heaviside step function and . This system is of the FitzHugh-Nagumo type and has several applications including nerve conduction and distributed chemical/ biochemical systems. It is demonstrated that this system exhibits a threshold phenomenon. This is done by considering the curve s(t) defined by s(t) = sup{x: v(x, t) = a}. The initial datum, ?(x), is said to be superthreshold if limt→∞ s(t) = ∞. It is proven that the initial datum is superthreshold if ?(x) > a on a sufficiently long interval, ?(x) is sufficiently smooth, and ?(x) decays sufficiently fast to zero as . 相似文献
4.
Jean-Luc Joly François de Thelin 《Journal of Mathematical Analysis and Applications》1976,54(1):230-244
We consider functionals of the form: If(u) = ∝Tf[t, u(t)]μ(dt), which are defined on spaces Lp(T, Rk), and we study for these functionals the properties of a convergence for which the conjugacy is a continuous operator. 相似文献
5.
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
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.
Felix Albrecht Harry Gatzke Abraham Haddad Nelson Wax 《Journal of Mathematical Analysis and Applications》1976,53(3):578-603
We study the time optimal control of the system , where x1 is the size of the population of one species, x2 is the population size of the second species, ?1 and ?2 are the fractional growth rates of the respective species, g1 and g2 are nowhere vanishing functions of class C1(0, + ∞), and the control u(t) = (u1(t), u2(t)) takes on values in a closed rectangle. The functions ?1 and ?2 are chosen to represent prey-predator, competitive, and symbiotic interactions.We show, for the various interactions, that a time optimal control, if it exists, must be “bang-bang,” and give sufficient conditions for the controllability, and for the existence, of time optimal controls of the above system. 相似文献
10.
The integral transform , where α and β are real, of pairs of special analytic functions f(z) = z + ···, g(z) = z + ···, univalent in the open unit disc Δ is studied. The transform and our results extend some recent results due to Shirakova. 相似文献
11.
Yasuhiro Takeuchi Norihiko Adachi 《Journal of Mathematical Analysis and Applications》1981,79(1):141-162
This paper presents sufficient conditions for the existence of a nonnegative and stable equilibrium point of a dynamical system of Volterra type, (1) , for every q = (q1,…, qn)T?Rn. Results of a nonlinear complementarity problem are applied to obtain the conditions. System (1) has a nonnegative and stable equilibrium point if (i) f(x) = (f1(x),…,fn(x))T is a continuous and differentiable M-function and it satisfies a certain surjectivity property, or (ii), f(x) is continuous and strongly monotone on R+0n. 相似文献
12.
Teruo Ikebe 《Journal of Functional Analysis》1975,20(2):158-177
A spectral representation for the self-adjoint Schrödinger operator H = ?Δ + V(x), x? R3, is obtained, where V(x) is a long-range potential: , grad , being the Laplace-Beltrami operator on the unit sphere Ω. Namely, we shall construct a unitary operator from PL2(R3) onto being the orthogonal projection onto the absolutely continuous subspace for H, such that for any Borel function α(λ), . 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.
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
15.
Hans G Kaper 《Journal of Mathematical Analysis and Applications》1977,59(3):415-422
In this paper the integrals are investigated for positive real values of the variable τ. Here, m is a nonnegative integer, v is a complex variable with Re(v) > ?1. Both integrals are related to the complex integral Φmγ(z) = ∝0∞exp[?(t ? z)]t?γ(ln t)m(t ? z)?1dt with 0 ? Re(γ) < 1, the behavior of which is analyzed in detail. The results are applied to obtain asymptotic representations for fmn(τ) and gmn(τ), m and n both nonnegative integers, near τ = 0. The latter integrals play a role in the study of the equations of neutron transport and radiative transfer. 相似文献
16.
Alan McIntosh 《Journal of Functional Analysis》1985,61(3):307-327
Consider an elliptic sesquilinear form defined on × by , where is a closed subspace of which contains , Ω is a bounded Lipschitz domain in n, for all ζ?n with ¦ζ¦ = 1. Let L be the operator with largest domain satisfying J[u, v] = (Lu, v) for all υ∈. Then L + λI is a maximal accretive operator in for λ a sufficiently large real number. It is proved that is a bounded operator from to provided mild regularity of the coefficients is assumed. In addition it is shown that if the coefficients depend differentiably on a parameter t in an appropriate sense, then the corresponding square root operators also depend differentiably on t. The latter result is new even when the forms J are hermitian. 相似文献
17.
Eng-Bin Lim 《Journal of Differential Equations》1978,30(1):49-53
The author discusses the best approximate solution of the functional differential equation x′(t) = F(t, x(t), x(h(t))), 0 < t < l satisfying the initial condition x(0) = x0, where x(t) is an n-dimensional real vector. He shows that, under certain conditions, the above initial value problem has a unique solution y(t) and a unique best approximate solution of degree k (cf. [1]) for a given positive integer k. Furthermore, , where ¦ · ¦ is any norm in Rn. 相似文献
18.
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
19.
Charles J Monlezun 《Journal of Mathematical Analysis and Applications》1974,47(1):133-152
A theory of scattering for the time dependent evolution equations (1) is developed. The wave operators are defined in terms of the evolution operators Uj(t, s), which govern (1). The scattering operator remains unitary. Sufficient conditions for existence and completeness of the wave operators are obtained; these are the main results. General properties, such as the chain rule and various intertwining relations, are also established. Applications include potential scattering (H0(t) = ?Δ, Δ denoting the Laplacian, and H1(t) = ?Δ + q(t, ·)) and scattering for second-order differential operators with coefficients constant in the spatial variable (). 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