Application of the regularization method to solve an inverse problem of non-linear heat-conduction theory

Glasko, V. B.; Zakharov, M. V.; Kolp, A. Ya.

doi:10.1016/0041-5553(75)90222-0

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H« X (O-)h1

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1982

1993

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Cited by 4 publications

(2 citation statements)

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“…Stability estimates have been obtained, by methods quite different from ours and in a different functional setting, by Cannon [2], [3], [4], [5]. Similar problems have been discussed by Anderssen and Saull [1], Glasko, Zaharov and Kolp [6] and P. Manselli and K. Miller [7].…”

Section: Introductionmentioning

confidence: 68%

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A note on an ill-posed problem for the heat equation

Talenti¹,

Vessella²

1982

J Aust Math Soc A

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In this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation u, -u xx = 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x -xj,... ,x = x n , are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0. 1980 Mathematics subject classification (Amer. Math. Soc): 35 K 05.

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Section: Introductionmentioning

confidence: 68%

“…As 0(A)/X increases with X, (2.12) and (1.6) give (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) In view of the expansion of (/>"' (see lemma below) the estimates (i), (ii) have been established.…”

Section: H« X (O-)hmentioning

confidence: 98%