Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Uniqueness theorem for the solution of the inverse problem for a generalized kinetic equation

Uniqueness theorem for the solution of the inverse problem for a generalized kinetic equation /. Inv. Hi-Posed Problems, Vol.3, No.5, pp.383-391 (1995) © VSP 1995 V.G. BARDAKOV* Received July 26, 1995 Abstract -- We investigate the inverse problem for a generalized kinetic equation and prove that this problem has no more than one solution if some matrices dependent on the equation coefficients are positive definite. We also prove a differential identity which may be useful when solving inverse problems of mathematical physics. Let Q be a domain of the real Euclidean space R n+1 , n > 1, for variables (x,0> where = (xi,...,x n ) G K n , \Xi -- *·\ < ,·, i = 1, ...,n, and a variable t G R satisfies the inequality \t - tQ\ < b. We assume that a, > 0 and 6 > 0, x*· and *o are fixed numbers. We consider the generalized kinetic equation in the domain Q, \(x,t) (1) where ufdw dH dw 9H akl = a*'(x), akl = -alk , *,/ = , . , . , is an operator of the Poisson bracket type and the right-hand side (, t) satisfies the equation We pose the inverse problem. Find functions W(x, t) and (, t) defined in the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

Uniqueness theorem for the solution of the inverse problem for a generalized kinetic equation

Loading next page...
 
/lp/de-gruyter/uniqueness-theorem-for-the-solution-of-the-inverse-problem-for-a-mVRrNU38P7

References (3)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0928-0219
eISSN
1569-3945
DOI
10.1515/jiip.1995.3.5.383
Publisher site
See Article on Publisher Site

Abstract

/. Inv. Hi-Posed Problems, Vol.3, No.5, pp.383-391 (1995) © VSP 1995 V.G. BARDAKOV* Received July 26, 1995 Abstract -- We investigate the inverse problem for a generalized kinetic equation and prove that this problem has no more than one solution if some matrices dependent on the equation coefficients are positive definite. We also prove a differential identity which may be useful when solving inverse problems of mathematical physics. Let Q be a domain of the real Euclidean space R n+1 , n > 1, for variables (x,0> where = (xi,...,x n ) G K n , \Xi -- *·\ < ,·, i = 1, ...,n, and a variable t G R satisfies the inequality \t - tQ\ < b. We assume that a, > 0 and 6 > 0, x*· and *o are fixed numbers. We consider the generalized kinetic equation in the domain Q, \(x,t) (1) where ufdw dH dw 9H akl = a*'(x), akl = -alk , *,/ = , . , . , is an operator of the Poisson bracket type and the right-hand side (, t) satisfies the equation We pose the inverse problem. Find functions W(x, t) and (, t) defined in the

Journal

Journal of Inverse and Ill-Posed Problemsde Gruyter

Published: Jan 1, 1995

There are no references for this article.