Regularization by Nonlocal Conditions of the Incorrect Problems for Differential‐operator Equations of the First Order

Yurchuk, N. I.; Mousa, Ababneh

doi:10.3846/13926292.1997.9637080

Cited by 2 publications

(3 citation statements)

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“…Note that, in this work, using a quasiboundary value method, we study the nonhomogeneous differential-operator equation introducing nonlocal conditions. e results given in this paper generalized the results of the work given by Yurchuk and Ababneh [8] where they considered the homogeneous case. [10][11][12][13][14][15][16]…”

Section: The Convergence Resultssupporting

confidence: 77%

“…then the function u ε (t) can be written as follows: 3) is well-posed, and its unique solution is u ε (t) given by (8). Furthermore,…”

Section: The Approximate Problemmentioning

confidence: 99%

“…We mention that the same problem for the homogeneous equation is treated by Yurchuk and Ababneh [8] and by Bessila [9] by introducing different nonlocal conditions.…”

Section: Introductionmentioning

confidence: 99%

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An Approximate Solution for a Class of Ill-Posed Nonhomogeneous Cauchy Problems

Teniou

Djezzar

2021

Journal of Mathematics

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In this paper, we consider a nonhomogeneous differential operator equation of first order u ′ t + A u t = f t . The coefficient operator A is linear unbounded and self-adjoint in a Hilbert space. We assume that the operator does not have a fixed sign. We associate to this equation the initial or final conditions u 0 = Φ or u T = Φ . We note that the Cauchy problem is severely ill-posed in the sense that the solution if it exists does not depend continuously on the given data. Using a quasi-boundary value method, we obtain an approximate nonlocal problem depending on a small parameter. We show that regularized problem is well-posed and has a strongly solution. Finally, some convergence results are provided.

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Section: The Convergence Resultssupporting

confidence: 77%

“…then the function u ε (t) can be written as follows: 3) is well-posed, and its unique solution is u ε (t) given by (8). Furthermore,…”

Section: The Approximate Problemmentioning

confidence: 99%