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Entire solutions of the abstract cauchy problem 总被引:3,自引:0,他引:3
Ralph deLaubenfels 《Semigroup Forum》1991,42(1):83-105
We introduce a family of operators that we will callentire C-groups, and apply them to the first and second order abstract Cauchy problem, for a large class of linear operators on a Banach
space. This produces unique solutions, for all initial data in a large (often dense) set, eachof which extends to an entire
function, with continuous dependence on the initial data.
Applications include the backward heat equation and the Cauchy problem for the Laplace equation. 相似文献
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Guoxiang Chen Meiying Wang 《分析论及其应用》2007,23(3):266-273
For a continuous, increasing function ω: R → R \{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that [ω(t)]-1u(t,x) is uniformly continues on R , and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A|z(A,ω) generates an O(ω(t))strongly continuous cosine operator function family. 相似文献
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LetA be the infinitesimal generator of aC
0 semigroup in a Banach spaceE. We obtain necessary conditions for a solution of the Cauchy problem {fx112-1} to be classical for arbitrary ϕ εC([0,T]) andf εE. 相似文献
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给出了n次积分C半群的几个性质及其证明,讨论了它与一类抽象柯西问题存在强解的关系及强解的表示式. 相似文献
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Mingchu Gao 《数学学报(英文版)》1999,15(4):535-548
In this paper, we first give a sufficient and necessary condition for
to generate an exponentially bounded
-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem ((ACP2) for short) in some sense. Then we use these results and those in [1] to discuss the C-(exponential) wellposedness of a kind of (ACP2) with application backgrounds, and develop the results in [2].
This project is supported by the NNSF of China, and the Youth Science and Technique Foundation of Shanxi Province, China 相似文献
9.
Jaime Cruz-Sampedro 《Mathematische Zeitschrift》2001,237(4):727-735
We prove a conjecture of Agmon on the unique continuation “at infinity” of solutions to certain second-order differential
inequalities in Hilbert spaces. Our result extends previous work of J?ger.
Received: 29 June 1998; in final form: 1 December 1999 /Published online: 25 June 2001 相似文献
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A. E. Zernov 《Ukrainian Mathematical Journal》1991,43(2):161-167
We consider the Cauchy problem (x)n=atr + bx + f(t, x, x), x(0)=0. We prove the existence of continuously differentiable solutions and study their asymptotic behavior for t + 0.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 187–193, February, 1991. 相似文献
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《复变函数与椭圆型方程》2012,57(10):703-709
We consider an abstract version of the Cauchy–Kowalewski Problem with the right-hand side being free from the Lipschitz-type conditions, and prove the existence theorem. 相似文献
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Summary We study existence, uniqueness and regularity of the strict, classical and strong solution u C([0,T],E) of the non-autonomous evolution equation u(t)–A(t)u(t)= f(t), with the initial datum, u(0)=x, in a Banach space E, where {A(t)} is a family of infinitesimal generators of analytic semi-groups whose domains are constant in t and possibly not dense in E. We prove necessary and sufficient conditions for existence and Hölder regularity of the solutions and their first derivative. 相似文献
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E. V. Radkevich 《Journal of Mathematical Sciences》2012,181(2):232-280
We prove the existence of global solutions to discrete kinetic equations. We also derive an expansion of the solution and
investigate the influence of oscillations generated by the interaction operator. 相似文献
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Yang Haitao 《Journal of Differential Equations》2003,189(2):487-512
The following singular elliptic boundary value problem is studied:
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In this paper, a new approach is provided to study the asymptotic behavior of functions. A Tauberian theorem is improved and applied to describe the asymptotic behavior of abstract functional differential equations of the form
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In this paper, we study the Cauchy problem of the Cahn–Hilliard equation, and first reveal that the complicated asymptotic behavior of solutions can happen in high-order parabolic equation. 相似文献