Estimates in C 2l,l for solution of a boundary value problem for the nonstationary stokes system with a surface tension in boundary condition

1992 ◽  
pp. 284-290
Author(s):  
Il'ia Mogilevskii
Keyword(s):  
Boundary Condition ◽  
Surface Tension ◽  
Boundary Value Problem ◽  
Stokes System ◽  
Boundary Value

About one boundary value problem for the equations of heat and mass transfer with normal derivatives of the third order in the boundary condition

2021 ◽  
Vol 143 (2) ◽  
pp. 113-119
Author(s):  
Y. Khairullin ◽  
◽  
G. Tulesheva ◽  
A. Shakulikova ◽  
◽  
...  
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Heat And Mass Transfer ◽  
Boundary Value ◽  
Third Order ◽  
The Third ◽  
Derivatives Of

scholarly journals Some spectral properties of a boundary value problem with a spectral parameter in the boundary condition

2006 ◽  
Vol 74 (3) ◽  
pp. 883-886 ◽  
Author(s):  
N. B. Kerimov ◽  
Z. S. Aliev
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Spectral Properties ◽  
Boundary Value

scholarly journals Wellposedness of Neumann boundary-value problems of space-fractional differential equations

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Hong Wang ◽  
Danping Yang
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Neumann Boundary Condition ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Fractional Differential ◽  
Neumann Boundary Value Problems ◽  
Well Posed

AbstractFractional differential equation (FDE) provides an accurate description of transport processes that exhibit anomalous diffusion but introduces new mathematical difficulties that have not been encountered in the context of integer-order differential equation. For example, the wellposedness of the Dirichlet boundary-value problem of one-dimensional variable-coefficient FDE is not fully resolved yet. In addition, Neumann boundary-value problem of FDE poses significant challenges, partly due to the fact that different forms of FDE and different types of Neumann boundary condition have been proposed in the literature depending on different applications.We conduct preliminary mathematical analysis of the wellposedness of different Neumann boundary-value problems of the FDEs. We prove that five out of the nine combinations of three different forms of FDEs that are closed by three types of Neumann boundary conditions are well posed and the remaining four do not admit a solution. In particular, for each form of the FDE there is at least one type of Neumann boundary condition such that the corresponding boundary-value problem is well posed, but there is also at least one type of Neumann boundary condition such that the corresponding boundary-value problem is ill posed. This fully demonstrates the subtlety of the study of FDE, and, in particular, the crucial mathematical modeling question: which combination of FDE and fractional Neumann boundary condition, rather than which form of FDE or fractional Neumann boundary condition, should be used and studied in applications.

scholarly journals An Approximate Grid Solution of a Nonlocal Boundary Value Problem with Integral Boundary Condition for Laplace's Equation

2018 ◽  
Vol 22 ◽  
pp. 01016 ◽  
Author(s):  
Adıgüzel A. Dosiyev ◽  
Rifat Reis
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Condition ◽  
Unknown Boundary ◽  
Laplace’S Equation ◽  
Nonlocal Boundary Value Problem ◽  
Integral Boundary ◽  
Laplace's Equation

A new method for the solution of a nonlocal boundary value problem with integral boundary condition for Laplace's equation on a rectangular domain is proposed and justified. The solution of the given problem is defined as a solution of the Dirichlet problem by constructing the approximate value of the unknown boundary function on the side of the rectangle where the integral boundary condition was given. Further, the five point approximation of the Laplace operator is used on the way of finding the uniform estimation of the error of the solution which is order of 0(h2), where hi s the mesh size. Numerical experiments are given to support the theoretical analysis made.

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