Fundamental solutions of hypoelliptic boundary value problems

1974 ◽  
pp. 139-146
Author(s):  
J. Barros Neto
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Fundamental Solutions

scholarly journals An axially symmetric forced convection problem

1975 ◽  
Vol 20 (1) ◽  
pp. 1-17
Author(s):  
J. A. Belward
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Convection Heat Transfer ◽  
Fundamental Solutions ◽  
Integral Representations ◽  
Original Equation ◽  
Transfer Model ◽  
Axially Symmetric ◽  
Simple Diffusion ◽  
Diffusion Convection

AbstractA simple diffusion-convection heat transfer model is formulated which leads to an axially symmetric partial differential equation. The equation is shown to be closely related to a second one which is adjoint to the original equation in one variable can and be interpreted as a description of another diffusion-convection model. Fundamental solutions of the original equation are constructed and interpreted with reference to both models. Some boundary value problems are solved in series form and integral representations of the solutions are also given. The boundary value problems are shown to be equivalent to an integral equation and the correspondence between the two formulations is understood in terms of the two diffusion-convection problems. A Péclet number is defined in one of the boundary value problems and the behaviour of the solutions is studied for large and small values of this parameter.

scholarly journals Solution of inverse non-stationary boundary value problems of diffraction of plane pressure wave on convex surfaces based on analytical solution

2020 ◽  
Vol 18 (4) ◽  
pp. 676-680
Author(s):  
Olga Egorova ◽  
Ko Ye
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problems ◽  
Pressure Wave ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
The Body ◽  
Parabolic Cylinder ◽  
Pressure Jump ◽  
Stationary Boundary ◽  
Special Cases

Research in the field of unsteady interaction of shock waves propagating in continuous media with various deformable barriers are of considerable scientific interest, since so far there are only a few scientific works dealing with solving problems of this class only for the simplest special cases. In this work, on the basis of analytical solution, we study the inverse non-stationary boundary-value problem of diffraction of plain pressure wave on convex surface in form of parabolic cylinder immersed in liquid and exposed to plane acoustic pressure wave. The purpose of the work is to construct approximate models for the interaction of an acoustic wave in an ideal fluid with an undeformable obstacle, which may allow obtaining fundamental solutions in a closed form, formulating initial-boundary value problems of the motion of elastic shells taking into account the influence of external environment in form of integral relationships based on the constructed fundamental solutions, and developing methods for their solutions. The inverse boundary problem for determining the pressure jump (amplitude pressure) was also solved. In the inverse problem, the amplitude pressure is determined from the measured pressure in reflected and incident waves on the surface of the body using the least squares method. The experimental technique described in this work can be used to study diffraction by complex obstacles. Such measurements can be beneficial, for example, for monitoring the results of numerical simulations.

scholarly journals Fundamental solutions and surface distributions

1969 ◽  
Vol 16 (3) ◽  
pp. 255-257
Author(s):  
R. A. Adams ◽  
G. F. Roach
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Bounded Domain ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Second Order ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Image Position

When studying the solutions of elliptic boundary value problems in a bounded, smoothly bounded domain D⊂Rn we often encounter the formulawhere u(x)∈C2(D)∩C′(D̄) is a solution of the second order self-adjoint elliptic equationand denotes differentiation along the inward normal to ∂D at x∈∂D.

Fundamental Solutions for Two-Point Boundary Value Problems in Orbital Mechanics

2016 ◽  
Vol 77 (1) ◽  
pp. 129-172 ◽  
Author(s):  
Seung Hak Han ◽  
William M. McEneaney
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Orbital Mechanics ◽  
Point Boundary
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