Nonlocal boundary-value problem for linear partial differential equations unsolved with respect to the higher time derivative

2007 ◽  
Vol 59 (3) ◽  
pp. 409-422
Author(s):  
O. D. Vlasii ◽  
B. I. Ptashnyk
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Time Derivative ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Partial Differential ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document