Introduction to Delay Partial Differential Equations

2019 ◽  
pp. 37-67
Author(s):  
W. E. Schiesser
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Delay Partial Differential Equations

scholarly journals Numerical method for singularly perturbed delay parabolic partial differential equations

2017 ◽  
Vol 21 (4) ◽  
pp. 1595-1599 ◽  
Author(s):  
Yulan Wang ◽  
Dan Tian ◽  
Zhiyuan Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Present Method ◽  
Singularly Perturbed ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Numerical Examples ◽  
Barycentric Interpolation ◽  
Delay Partial Differential Equations

The barycentric interpolation collocation method is discussed in this paper, which is not valid for singularly perturbed delay partial differential equations. A modified version is proposed to overcome this disadvantage. Two numerical examples are provided to show the effectiveness of the present method.

ON EXPONENTIAL STABILITY FOR STOCHASTIC DELAY PARTIAL DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 09 (01) ◽  
pp. 121-134
Author(s):  
GUOSHENG YU ◽  
BING LIU
Keyword(s):  
Partial Differential Equations ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Hilbert Spaces ◽  
Stability Criteria ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Finite Delay ◽  
Delay Partial Differential Equations

This paper is concerned with the exponential stability of energy solutions to a nonlinear stochastic delay partial differential equations with finite delay in separable Hilbert spaces. Some exponential stability criteria are obtained by constructing the Lyapunov function. As an application, one example is also given to illustrate our results.

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