One Goursat problem in a Sobolev space

Mamedov, Ilgar G.

doi:10.3103/s1066369x1102006x

“…This is connected with the fact that in the statement of problem (1), (2) the right sides of Cauchy conditions don't require additional conditions of agreement type. Note that such boundary value problems in non-classical treatment were considered in the author's papers [13][14][15][16][17].…”

Section: Resultsmentioning

confidence: 99%

Cauchy Problem in the Non-Classical Treatment for One Pseudoparabolic Equation

Mamedov¹

2014

ujcmj

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In the paper, we consider the Cauchy problem for a fifth order pseudoparabolic equation that appears in studying the issues of fluid filtration in fissured media, the moisture transfer in soils and etc. The Cauchy problem with non-classic conditions not requiring the agreement conditions are studied for a discontinuous coefficient pseudoparabolic equation. The equivalence of these conditions with the Cauchy classic condition is substantiated in the case when the solution of the stated problem is sought in S.L.Sobolev anisotropic space

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“…It should be especially noted that in the papers [6][7] the author suggested a method for investigating boundary value problems in non-classical treatment for pseudoparabolic equations with non-smooth coefficients of higher order.…”

Section: Fig 2 Geometrical Interpretation Of Dirichlet Non-classicamentioning

confidence: 99%

“…The matter is that in this case, for the existence of the solution it is necessary that the conditions ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) This is an advantage of problem (1), (2) compared to non-classic statement of Cauchy problem (1), (3). Note that some problems in non-classical treatment for pseudoparabolic equations were investigated in the papers of the author's [11][12][13][14].…”

Section: Problem Statementmentioning

confidence: 99%

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Neumann problem in the non-classical treatment for a fourth order pseudoparabolic equation

Mamedov

¹

2012

2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI)

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In the paper, we consider the Cauchy problem for a fifth order pseudoparabolic equation that appears in studying the issues of fluid filtration in fissured media, the moisture transfer in soils and etc. The Cauchy problem with non-classic conditions not requiring the agreement conditions are studied for a discontinuous coefficient pseudoparabolic equation. The equivalence of these conditions with the Cauchy classic condition is substantiated in the case when the solution of the stated problem is sought in S.L.Sobolev anisotropic space.

show abstract

“…This is connected with the fact that in the statement of problem ( 1), ( 4), the right sides of boundary conditions don't require additional conditions of agreement type. Note that some boundary value problems in non-classic treatments were considered in the author's papers [7][8][9].…”

mentioning

confidence: 99%