Solution of initial-boundary value problem for a system of partial differential equations of the third order

2019 ◽  
Vol 63 (4) ◽  
pp. 12-22 ◽  
Author(s):  
A. T. Assanova
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Third Order ◽  
Partial Differential ◽  
The Third ◽  
Initial Boundary Value

scholarly journals Initial-Boundary Value Problem for Fractional Partial Differential Equations of Higher Order

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Djumaklych Amanov ◽  
Allaberen Ashyralyev
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Partial Differential ◽  
Initial Boundary Value ◽  
The Right

The initial-boundary value problem for partial differential equations of higher-order involving the Caputo fractional derivative is studied. Theorems on existence and uniqueness of a solution and its continuous dependence on the initial data and on the right-hand side of the equation are established.

Weak solutions to the initial-boundary value problem for the shearing of non-homogeneous thermoviscoplastic materials

1989 ◽  
Vol 113 (3-4) ◽  
pp. 257-265 ◽  
Author(s):  
Nicolas Charalambakis ◽  
François Murat
Keyword(s):  
Weak Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Temperature Dependent ◽  
Initial Boundary Value

SynopsisWe prove the existence of a weak solution for the system of partial differential equations describing the shearing of stratified thermoviscoplastic materials with temperature-dependent non-homogeneous viscosity.

Solution of a problem for a system of third order partial differential equations

2021 ◽  
pp. 68-76
Author(s):  
Vladimir I. Uskov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Formula ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Third Order ◽  
Partial Differential ◽  
Degenerate Operator ◽  
Initial Boundary Value ◽  
Third Derivative

An initial-boundary value problem for a system of third-order partial differential equations is considered. Equations and systems of equations with the highest mixed third derivative describe heat exchange in the soil complicated by the movement of soil moisture, quasi-stationary processes in a two-component semiconductor plasma, etc. The system is reduced to a differential equation with a degenerate operator at the highest derivative with respect to the distinguished variable in a Banach space. This operator has the property of having 0 as a normal eigenvalue, which makes it possible to split the original equations into an equation in subspaces. The conditions are obtained under which a unique solution to the problem exists; the analytical formula is found.

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