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

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.

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Initial-boundary value problems for a time-fractional differential equation with involution perturbation

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2019014 ◽

2019 ◽

Vol 14 (3) ◽

pp. 312 ◽

Cited By ~ 1

Author(s):

Nasser Al-Salti ◽

Sebti Kerbal ◽

Mokhtar Kirane

Keyword(s):

Boundary Value Problems ◽

Separation Of Variables ◽

Boundary Value ◽

Nonlocal Boundary ◽

Initial Boundary ◽

Nonlocal Boundary Conditions ◽

Initial Boundary Value Problems ◽

Initial Boundary Value ◽

Formal Solutions ◽

The Given

Direct and inverse initial-boundary value problems of a time-fractional heat equation with involution perturbation are considered using both local and nonlocal boundary conditions. Results on existence of formal solutions to these problems are presented. Solutions are expressed in a form of series expansions using appropriate orthogonal basis obtained by separation of variables. Convergence of series solutions are obtained by imposing certain conditions on the given data. Uniqueness of the obtained solutions are also discussed. The obtained general solutions are illustrated by an example using an appropriate choice of the given data.

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Degenerate Differential Operators with Parameters

Abstract and Applied Analysis ◽

10.1155/2007/51410 ◽

2007 ◽

Vol 2007 ◽

pp. 1-27 ◽

Cited By ~ 12

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.

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