Modified Galerkin Method for the Second Order Equation of Mixed Type and Estimate of Its Error

Egorov, I. E.; Fedorov, Valery E.; Tikhonova, Irina M.

doi:10.14529/mmp160403

Cited by 4 publications

(4 citation statements)

References 1 publication

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“…be eigenfunctions of the problem (5), corresponding respectively to positive and negative λ + k , λ − k eigenvalues, and the number of λ + k , −λ − k form a increasing sequence. We denote by (u, v)…”

Section: Consider the Spectral Problemmentioning

confidence: 99%

“…Assume that the solution (v(x, t), u(x, t)) of problem (1)-(4) exists. Then for the system (1) using the properties of eigenfunctions of the problem (5) and the definition of a generalized solution, we have…”

Section: Consider the Spectral Problemmentioning

confidence: 99%

“…The theory of the solvability of boundary value problems for linear models described by a such equations has been constructed in the papers S. A. Tersenov, I. E. Egorov, A. A. Kerefov, N. V. Kislov, S. G. Pyatkov and others [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Conditional Correctness and Approximate Solution of Boundary Value Problem for the System of Second Order Mixed-type Equations

Khajiev¹,

Khazhiev²

2018

J. Sib. Fed. Univ., Math. phys.

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In this paper, we consider the system of second-order mixed type equations. Theorems of uniqueness and conditional stability in the set of correctness are proven. The approximate solution is constructed by the method of regularization and by the quasi-inverse method.Keywords: system of equations, boundary value problem, ill-posed problem, a priori estimate, theorem of the uniqueness, conditional stability, set of correctness, approximate solution, regularization.

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Section: Consider the Spectral Problemmentioning

confidence: 99%

Section: Consider the Spectral Problemmentioning

confidence: 99%

See 1 more Smart Citation

Conditional Correctness and Approximate Solution of Boundary Value Problem for the System of Second Order Mixed-type Equations

Khajiev¹,

Khazhiev²

2018

J. Sib. Fed. Univ., Math. phys.

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show abstract

“…A great contribution to the study of boundary value problems for equations of mixed type was made by A. I. Kozhanov [8], I. E. Egorov [9], S. G. Pyatkov [10,11], A. A. Kerefov [12], I. S. Pulkin [13], K. B. Sabitov [14], and others.…”

Section: Introductionmentioning

confidence: 99%

Ill-posed Boundary-value Problem for a System of Partial Differential Equations with Two Degenerate Lines

Fayazov

Khudayberganov

Фаязов³

et al. 2019

Journal of Siberian Federal University. Mathematics &Amp; Physics

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This paper is devoted to the investigation of ill-posed boundary-value problem for system of parabolic type equations with changing time direction with two degenerate lines. The problem under consideration is ill-posed in the sense of J. Hadamard, namely, there is no continuous dependence of the solution on the initial data. Such equations have many different applications, for example, describe the processes of heat propagation in inhomogeneous media, the interaction of filtration flows, mass transfer near the surface of an aircraft, and the description of complex viscous fluid flows. As possible applications should also indicate the task of calculating heat exchangers, in which the counter flow principle is used. Theorems on the uniqueness and conditional stability of a solution on a set of well-posedness are proved. We construct a sequence of approximate (regularized) solutions that are stable on the set of well-posedness.

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The Galerkin method for nonclassical equations of mathematical physics

Egorov

Fedorov

Tikhonova

et al. 2017

AIP Conference Proceedings

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Modified Galerkin Method for the Second Order Equation of Mixed Type and Estimate of Its Error

Cited by 4 publications

References 1 publication

Conditional Correctness and Approximate Solution of Boundary Value Problem for the System of Second Order Mixed-type Equations

Conditional Correctness and Approximate Solution of Boundary Value Problem for the System of Second Order Mixed-type Equations

Ill-posed Boundary-value Problem for a System of Partial Differential Equations with Two Degenerate Lines

The Galerkin method for nonclassical equations of mathematical physics

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