Lax’s Construction of Parametrices of Fundamental Solutions of Strongly Hyperbolic Operators, its Prehistory and Posthistory

1987 ◽  
pp. 60-73 ◽  
Author(s):  
Lars Gårding
Keyword(s):  
Fundamental Solutions ◽  
Hyperbolic Operators

Fundamental solutions of a class of ultra-hyperbolic operators on pseudo H-type groups

2020 ◽  
Vol 369 ◽  
pp. 107186
Author(s):  
Wolfram Bauer ◽  
André Froehly ◽  
Irina Markina
Keyword(s):  
Fundamental Solutions ◽  
Hyperbolic Operators

Improved geometric modeling using the method of fundamental solutions

2021 ◽  
Vol 130 ◽  
pp. 49-57
Author(s):  
C.S. Chen ◽  
Lionel Amuzu ◽  
Kwesi Acheampong ◽  
Huiqing Zhu
Keyword(s):  
Geometric Modeling ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

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