On the solvability of the tricomi problem for the Lavrent’ev-Bitsadze equation with mixed boundary conditions

Moiseev, T. E.

doi:10.1134/s0012266109100206

Cited by 9 publications

(5 citation statements)

References 1 publication

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“…Now, we improve estimate (18) in Theorem 2.2 and prove the following Theorem, which shows what is the maximal possible singularity of the solution U(ξ , η) around the point (1, 1). Theorem 2.3 Let β ∈ (0, 1) and F ∈ C(D) ∩ C 1 (D \ (1, 1)), then for the solution U(ξ , η) of the Problem PK 2 in D ε the following a priori estimate holds: for each µ > 0, there exists a constant C µ > 0, independent of function F, such that…”

Section: Remark 21 We Mention Here That Investigation Of the Prottermentioning

confidence: 96%

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Singular solutions to Protter problem for Keldysh type equations

Hristov¹

2014

AIP Conference Proceedings

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Three-dimensional boundary value problem for equations of Keldysh type is studied. It is known that this problem is not well-posed, since it has infinite-dimensional co-kernel. In the present paper it is shown that for n ∈ N there exist a smooth right-hand side function f n , for which the corresponding unique generalized solution has a strong power-type singularity. This singularity is isolated at the vertex O of the inner characteristic surface and does not propagate along the surface. As well as, an exact a priory estimate for unique generalized solution is stated.

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Section: Remark 21 We Mention Here That Investigation Of the Prottermentioning

confidence: 96%

“…When equations are considered only in the hyperbolic part of the original Protter domain we arrived to the Protter problems in domain Ω m . For results concerning uniqueness and existence or nonexistence of nontrivial solutions to related problems for hyperbolic-elliptic type equations see [2,3,6,[14][15][16][17][18]27].…”

Section: Introductionmentioning

confidence: 99%

Singular solutions to Protter problem for Keldysh type equations

Hristov¹

2014

AIP Conference Proceedings

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“…Results for uniqueness are obtained by A. Aziz and M. Schneider [2], but up to now not a single example of nontrivial solution of the new problem, neither a general existence result is known. Some different statements of Darboux type problems in R 3 or some connected with them Protter problem for mixed type equations are investigated by A.Bitsadze [4], J. Barros-Neto and I. Gelfand [3], D. Lupo, C. Morawetz and K. Payne [11], D. Lupo, K. Payne, N. Popivanov [12], T. E. Moiseev [13], J. Rasiass [18], D. Edmunds, N. Popivanov [5], B. Keyfitz, A. Tesdall, K. Payne, N. Popivanov [19].…”

Section: History Of the Protter Problemsmentioning

confidence: 99%

On uniqueness of quasi-regular solutions to Protter problem for Keldish type equations

Hristov¹,

Popivanov²,

Schneider³

2013

AIP Conference Proceedings

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“…Find a solution U of the problem (17), (18) in D (1) ε . (4) leads to similar 2-D Problem with the same differential equation (17).…”

Section: The Identitiesmentioning

confidence: 99%

“…We mention here papers of J. Barros-Neto and I. Gelfand [3], L. Dechevski and N. Popivanov [6], D. Lupo, C. Morawetz and K. Payne [15], D. Lupo, K. Payne, N. Popivanov [16] and [17], T. E. Moiseev [18], J. Rasiass [26], B. Keyfitz, A. Tesdall, K. Payne, N. Popivanov [14].…”

Section: Introduction and Statement Of The Problemmentioning

confidence: 99%