Time asymptotics for the biharmonic wave equation in exterior domains

1997 ◽  
Vol 15 (3-4) ◽  
pp. 359-384 ◽  
Author(s):  
Peter H. Lesky
Keyword(s):  
Wave Equation ◽  
Exterior Domains ◽  
Time Asymptotics

8.—Constructive Methods for Solving the Exterior Neumann Problem for the Reduced Wave Equation in a Spherically Symmetric Medium

1976 ◽  
Vol 75 (2) ◽  
pp. 97-107 ◽  
Author(s):  
David Colton ◽  
Wolfgang Wendland
Keyword(s):  
Wave Equation ◽  
Integral Operator ◽  
Neumann Problem ◽  
Acoustic Waves ◽  
Homogeneous Medium ◽  
Radiation Condition ◽  
Spherically Symmetric ◽  
Exterior Domains ◽  
Constructive Methods ◽  
Scattering Of Acoustic Waves

SYNOPSISAn integral operator is constructed which maps solutions of the reduced wave equation defined in exterior domains onto solutions of ∆n u+λ2(l+B(r))u = 0 (*) defined in exterior domains, where B(r) is a continuously differentiable function of compact support. This operator is then used to construct a solution to the exterior Neumann problem for (*) satisfying the Sommerfeld radiation condition at infinity. Such problems arise in connection with the scattering of acoustic waves in a non-homogeneous medium, and this paper gives a method for solving these problems which is suitable for analytic and numerical approximations.

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