An integral boundary-value problem in a layer for a system of linear partial differential equations

1995 ◽  
Vol 186 (11) ◽  
pp. 1671-1692 ◽  
Author(s):  
L V Fardigola
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Partial Differential ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Linear Partial Differential Equations

scholarly journals Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Josef Diblík ◽  
Denis Khusainov ◽  
Oleksandra Kukharenko ◽  
Zdeněk Svoboda
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Fourier Method ◽  
Parabolic Type ◽  
Second Order ◽  
Partial Differential ◽  
Order Linear ◽  
Linear Partial Differential Equations

The first boundary-value problem for an autonomous second-order system of linear partial differential equations of parabolic type with a single delay is considered. Assuming that a decomposition of the given system into a system of independent scalar second-order linear partial differential equations of parabolic type with a single delay is possible, an analytical solution to the problem is given in the form of formal series and the character of their convergence is discussed. A delayed exponential function is used in order to analytically solve auxiliary initial problems (arising when Fourier method is applied) for ordinary linear differential equations of the first order with a single delay.

Beam Vibrations With Time-Dependent Boundary Conditions

1950 ◽  
Vol 17 (4) ◽  
pp. 377-380
Author(s):  
R. D. Mindlin ◽  
L. E. Goodman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Time Dependent ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Vibration Problems

Abstract A procedure is described for extending the method of separation of variables to the solution of beam-vibration problems with time-dependent boundary conditions. The procedure is applicable to a wide variety of time-dependent boundary-value problems in systems governed by linear partial differential equations.

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