Analytical and numerical stability of partial differential equations with piecewise constant arguments

2013 ◽  
Vol 30 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Stability ◽  
Partial Differential ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant

scholarly journals Partial differential equations with piecewise constant delay

1991 ◽  
Vol 14 (3) ◽  
pp. 485-496 ◽  
Author(s):  
Joseph Wiener ◽  
Lokenath Debnath
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Abstract Cauchy Problem ◽  
Integral Transforms ◽  
Constant Delay ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Linear Partial Differential Equations ◽  
Piecewise Constant Argument ◽  
Constant Argument

The influence of certain discontinuous delays on the behavior of solutions to partial differential equations is studied. In Section 2, the initial value problems (IVP) are discussed for differential equations with piecewise constant argument (EPCA) in partial derivatives. A class of loaded partial differential equations that arise in solving certain inverse problems is studied in some detail in Section 3. Section 4 is devoted to obtain the solutions ofIVPfor linear partial differential equations with piecewise constant delay by using integral transforms. Finally, an abstract Cauchy problem is discussed.

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