On third order operator-differential equation with an operator boundary condition

2016 ◽  
Vol 10 ◽  
pp. 1031-1043
Author(s):  
Sabir S. Mirzoyev ◽  
Sevindj F. Babayeva
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Operator Differential Equation ◽  
Order Operator ◽  
Third Order

scholarly journals On the Stepanov-almost periodic solution of a second-order operator differential equation

1975 ◽  
Vol 19 (3) ◽  
pp. 261-263 ◽  
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Periodic Solution ◽  
Almost Periodic Solution ◽  
Second Order ◽  
Almost Periodicity ◽  
Operator Differential Equation ◽  
Almost Periodic ◽  
Order Operator ◽  
Image Position

Suppose X is a Banach space and J is the interval −∞<t<∞. For 1 ≦ p<∞, a function is said to be Stepanov-bounded or Sp-bounded on J if(for the definitions of almost periodicity and Sp-almost periodicity, see Amerio-Prouse (1, pp. 3 and 77).

Convolution Approximating Perfect Matched Layer Absorbing Boundary Condition of 3D Scalar Acoustic Wave Equation

2014 ◽  
Vol 971-973 ◽  
pp. 1095-1098
Author(s):  
Cong Wang ◽  
Jian Xun Zhang
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Wave Equation ◽  
Order Differential Equation ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Condition ◽  
Acoustic Wave Equation ◽  
Third Order ◽  
Absorbing Boundary ◽  
Perfect Matched Layer

Because traditional displacement form of 3D acoustic perfectly matched layer (PML) absorbing condition needs to split the displacement into three parts, which requires solving a third-order differential equation in time and occupies a large amount of memory. In order to solve the above problems, this paper puts forward an Convolution approximating PML absorbing boundary condition based on the previous works, and discusses the basic construction of the traditional perfectly matched layer absorbing boundary condition and the new arithmetic in detail, then the new method is compared with absorbing condition of low order paraxial approximation and traditional PML, investigating the absorbing effects of 3D acoustic wave’s numerical records.

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