Regularization of the Solution of the Cauchy Problem

Standard

Regularization of the Solution of the Cauchy Problem : The Quasi-Reversibility Method. / Romanov, V. G.; Bugueva, T. V.; Dedok, V. A.

In: Journal of Applied and Industrial Mathematics, Vol. 12, No. 4, 01.10.2018, p. 716-728.

Research output: Contribution to journal › Article › peer-review

Harvard

Romanov, VG, Bugueva, TV & Dedok, VA 2018, 'Regularization of the Solution of the Cauchy Problem: The Quasi-Reversibility Method', Journal of Applied and Industrial Mathematics, vol. 12, no. 4, pp. 716-728. https://doi.org/10.1134/S1990478918040129

APA

Romanov, V. G., Bugueva, T. V., & Dedok, V. A. (2018). Regularization of the Solution of the Cauchy Problem: The Quasi-Reversibility Method. Journal of Applied and Industrial Mathematics, 12(4), 716-728. https://doi.org/10.1134/S1990478918040129

Vancouver

Romanov VG, Bugueva TV, Dedok VA. Regularization of the Solution of the Cauchy Problem: The Quasi-Reversibility Method. Journal of Applied and Industrial Mathematics. 2018 Oct 1;12(4):716-728. doi: 10.1134/S1990478918040129

Author

Romanov, V. G. ; Bugueva, T. V. ; Dedok, V. A. / Regularization of the Solution of the Cauchy Problem : The Quasi-Reversibility Method. In: Journal of Applied and Industrial Mathematics. 2018 ; Vol. 12, No. 4. pp. 716-728.

BibTeX

@article{42f2791c7c2146d6beef0ea2fc80f19e,

title = "Regularization of the Solution of the Cauchy Problem: The Quasi-Reversibility Method",

abstract = "Some regularization algorithm is proposed related to the problem of continuation of the wave field from the planar boundary into the half-plane. We consider a hyperbolic equation whose main part coincideswith the wave operator, whereas the lowest term contains a coefficient depending on the two spatial variables. The regularization algorithm is based on the quasi-reversibility method proposed by Lattes and Lions. We consider the solution of an auxiliary regularizing equation with a small parameter; the existence, the uniqueness, and the stability of the solution in the Cauchy data are proved. The convergence is substantiated of this solution to the exact solution as the small parameter vanishes. A solution of an auxiliary problem is constructed with the Cauchy data having some error. It is proved that, for a suitable choice of a small parameter, the approximate solution converges to the exact solution.",

keywords = "Cauchy problem, continuation of the wave field, regularization",

author = "Romanov, {V. G.} and Bugueva, {T. V.} and Dedok, {V. A.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = oct,

day = "1",

doi = "10.1134/S1990478918040129",

language = "English",

volume = "12",

pages = "716--728",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - Regularization of the Solution of the Cauchy Problem

T2 - The Quasi-Reversibility Method

AU - Romanov, V. G.

AU - Bugueva, T. V.

AU - Dedok, V. A.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Some regularization algorithm is proposed related to the problem of continuation of the wave field from the planar boundary into the half-plane. We consider a hyperbolic equation whose main part coincideswith the wave operator, whereas the lowest term contains a coefficient depending on the two spatial variables. The regularization algorithm is based on the quasi-reversibility method proposed by Lattes and Lions. We consider the solution of an auxiliary regularizing equation with a small parameter; the existence, the uniqueness, and the stability of the solution in the Cauchy data are proved. The convergence is substantiated of this solution to the exact solution as the small parameter vanishes. A solution of an auxiliary problem is constructed with the Cauchy data having some error. It is proved that, for a suitable choice of a small parameter, the approximate solution converges to the exact solution.

AB - Some regularization algorithm is proposed related to the problem of continuation of the wave field from the planar boundary into the half-plane. We consider a hyperbolic equation whose main part coincideswith the wave operator, whereas the lowest term contains a coefficient depending on the two spatial variables. The regularization algorithm is based on the quasi-reversibility method proposed by Lattes and Lions. We consider the solution of an auxiliary regularizing equation with a small parameter; the existence, the uniqueness, and the stability of the solution in the Cauchy data are proved. The convergence is substantiated of this solution to the exact solution as the small parameter vanishes. A solution of an auxiliary problem is constructed with the Cauchy data having some error. It is proved that, for a suitable choice of a small parameter, the approximate solution converges to the exact solution.

KW - Cauchy problem

KW - continuation of the wave field

KW - regularization

UR - http://www.scopus.com/inward/record.url?scp=85058135053&partnerID=8YFLogxK

U2 - 10.1134/S1990478918040129

DO - 10.1134/S1990478918040129

M3 - Article

AN - SCOPUS:85058135053

VL - 12

SP - 716

EP - 728

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -

ID: 17831383