On boundary value problems for Maxwell set of equations in cylindrical domain

2014 ◽  
Vol 1 (2) ◽  
pp. 117-125 ◽  
Author(s):  
Nikolai Pleshchinskii ◽  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Cylindrical Domain ◽  
Maxwell Set

scholarly journals Degenerate Differential Operators with Parameters

2007 ◽  
Vol 2007 ◽  
pp. 1-27 ◽  
Author(s):  
Veli B. Shakhmurov
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Cylindrical Domain ◽  
Nonlocal Boundary Value Problems ◽  
Degenerate Elliptic ◽  
Systems Of Elliptic Equations ◽  
Principal Parts ◽  
Degenerate Differential Operator

The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valuedLp−spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.

scholarly journals WELL-POSEDNESS OF POINCARE PROBLEM IN THE CYLINDRICAL DOMAIN FOR A CLASS OF MULTI-DIMENSIONAL ELLIPTIC EQUATIONS

2017 ◽  
Vol 20 (10) ◽  
pp. 17-25
Author(s):  
S.A. Aldashev
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Singular Integral ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Cylindrical Domain ◽  
Second Order Elliptic Equations ◽  
Poincaré Problem ◽  
Well Posed

The boundary value problems for second order elliptic equations in domains with edges are well studied. For elliptic equations, boundary-value problems on the plane were shown to be well posed by using methods from the theory of analytic functions of complex variable. When the number of independent variables is greater than two, difficulties of fundamental nature arise. Highly attractive and convenient method of singular integral equations can hardly be applied, because the theory of multidimensional singular integral equations is still incomplete. In this paper with the help of the method suggested by the author, the unique solvability is shown and explicit form of classical solution of Poincare problem in a cylindrical domain for a one class of multidimensional elliptic equations is received.

scholarly journals Maximal regular boundary value problems in Banach-valued function spaces and applications

2006 ◽  
Vol 2006 ◽  
pp. 1-26 ◽  
Author(s):  
Veli B. Shakhmurov
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Maximal Regularity ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Cylindrical Domain ◽  
Initial Boundary Value Problems ◽  
Nonlocal Boundary Value Problems ◽  
Initial Boundary Value

The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valuedLp-spaces of these problems are given. By using these results, the maximal regularity of parabolic nonlocal initial boundary value problems is shown. In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.

scholarly journals Forced oscillations of solutions of parabolic equations

1987 ◽  
Vol 36 (2) ◽  
pp. 289-294 ◽  
Author(s):  
Norio Yoshida
Keyword(s):  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Forced Oscillations ◽  
Cylindrical Domain ◽  
All Solutions

Parabolic equations with forcing terms are studied and sufficient conditions are given that all solutions of boundary value problems are oscillatory in a cylindrical domain.

scholarly journals CORRECTNESS OF THE LOCAL BOUNDARY VALUE PROBLEM IN A CYLINDRICAL DOMAIN FOR ONE CLASS OF MULTIDIMENSIONAL ELLIPTIC EQUATIONS

2017 ◽  
Vol 22 (1-2) ◽  
pp. 7-17
Author(s):  
S. A. Aldashev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Singular Integral ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Classical Solutions ◽  
Cylindrical Domain ◽  
Local Boundary ◽  
Criterion Of Uniqueness

Correctness of boundary value problems in a plane for elliptical equations has been studied properly using the method of the theory of analytic functions. At investigation of analogous problems, when the number of independent variables is more than two, there arise principle difficulties. Quite good and convenient method of singular integral equations has to be abandoned because there is no complete theory of multidimensional singular integral equations. Boundary value problems for second-order elliptical equations in domains with edges have been studied properly earlier. Explicit classical solutions to Dirichlet and Poincare problems in cylindrical domains for one class of multidimensional elliptical equations can be found in the author’s works. In this article,the author proved that the local boundary value problem, which is the generalization of Dirichet and Poincare problem, has only solution. Besides, the criterion of uniqueness of regular solution is obtained.

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