用广义Sobolev方程正则化Banach空间中的后抛物型方程

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-07-28 DOI:10.1515/JIP-2012-0046

N. Duc, D. Hào, M. Shishlenin

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引用次数: 11

摘要

摘要设X为范数∥⋅∥{\| \cdot \|}的Banach空间{。设A:D≠(A)∧X→X A:D(A) \subset X \rightarrow X}是一个产生一致有界全纯半群的(可能无界的)算子。假设ε >{\varepsilon >}和T>{ T>}是两个给定的常数。求函数u的反抛物方程:[0,T]→X{ u:[0,T] \rightarrow X}满足u T +A²u= 0,0 本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations

Abstract Let X be a Banach space with norm ∥ ⋅ ∥ {\|\cdot\|} . Let A : D ⁢ ( A ) ⊂ X → X {A:D(A)\subset X\rightarrow X} be an (possibly unbounded) operator that generates a uniformly bounded holomorphic semigroup. Suppose that ε > 0 {\varepsilon>0} and T > 0 {T>0} are two given constants. The backward parabolic equation of finding a function u : [ 0 , T ] → X {u:[0,T]\rightarrow X} satisfying u t + A ⁢ u = 0 , 0 < t < T , ∥ u ⁢ ( T ) - φ ∥ ⩽ ε , u_{t}+Au=0,\quad 0

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography