scholarly journals Higher order asymptotic expansion of solutions to abstract linear hyperbolic equations

2020 ◽  
Author(s):  
Motohiro Sobajima
Keyword(s):  
Asymptotic Expansion ◽  
Hyperbolic Equations ◽  
Higher Order ◽  
Asymptotic Expansion Of Solutions ◽  
Linear Hyperbolic Equations

Multi-dimensional periodic problems for higher-order linear hyperbolic equations

2019 ◽  
Vol 26 (2) ◽  
pp. 235-256
Author(s):  
Tariel Kiguradze ◽  
Noha Al Jaber
Keyword(s):  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Dimensional Case ◽  
Well Posedness ◽  
Two Dimensional ◽  
Order Linear ◽  
Periodic Problems ◽  
Necessary And Sufficient ◽  
Linear Hyperbolic Equations

Abstract For higher-order linear hyperbolic equations the problem on periodic solutions is investigated. The concepts of associated problems, and α-well-posedness are introduced. Necessary and sufficient conditions of well-posedness in the two-dimensional case, as well as unimprovable sufficient conditions of well-posedness and α-well-posedness in the multi-dimensional case are established.

Fast high order ADER schemes for linear hyperbolic equations

2004 ◽  
Vol 197 (2) ◽  
pp. 532-539 ◽  
Author(s):  
Thomas Schwartzkopff ◽  
Michael Dumbser ◽  
Claus-Dieter Munz
Keyword(s):  
Hyperbolic Equations ◽  
High Order ◽  
Linear Hyperbolic Equations

The Higher Order Crack Tip Fields of Exponential Gradient FGMs Plates with Reissner’s Effect

2013 ◽  
Vol 278-280 ◽  
pp. 491-494
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Asymptotic Expansion ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Deformation ◽  
Plate Bending ◽  
Graded Materials ◽  
Fundamental Significance ◽  
Asymptotic Expansion Method

The Reissner’s plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials (FGMs) plates for a crack perpendicular to material gradient. The crack-tip higher order asymptotic fields of FGMs plates are obtained by the asymptotic expansion method. This study has fundamental significance as Williams’ solution.

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