scholarly journals Integro-differential systems with variable exponents of nonlinearity

2017 ◽  
Vol 15 (1) ◽  
pp. 859-883 ◽  
Author(s):  
Oleh Buhrii ◽  
Nataliya Buhrii
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Theorem ◽  
Fourth Order ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Exponents ◽  
Differential Systems ◽  
Initial Boundary Value

Abstract Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.

scholarly journals The analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers

2015 ◽  
Vol 3 ◽  
pp. 186
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stationary Problem ◽  
Elliptic Type ◽  
Exponential Spline ◽  
Initial Boundary Value

<p>In this paper we consider averaging methods for solving the 3-D boundary value problem in domain containing 2 layers of the peat block. We consider the metal concentration in the peat blocks. Using experimental data the mathematical model for calculation of concentration of metal in different points in every peat layer is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations of second order with piece-wise diffusion coefficients in every direction and peat layers.</p><p>The special parabolic and exponential spline, which interpolation middle integral values of piece-wise smooth function, are considered. With the help of this splines is reduce the problems of mathematical physics in 3-D with piece-wise coefficients to respect one coordinate to problems for system of equations in 2-D. This procedure allows reduce the 3-D problem to a problem of 2-D and 1-D problems and the solution of the approximated problem is obtained analytically.</p><p>The solution of corresponding averaged 2-D initial-boundary value problem is obtained also numerically, using for approach differential equations the discretization in space applying the central differences. The approximation of the 2-D non-stationary problem is based on the implicit finite-difference and alternating direction (ADI) methods. The numerical solution is compared with the analytical solution.</p>

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