Singular Boundary Integral Equations

2013 ◽  
pp. 103-140 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Singular Boundary

scholarly journals METHOD OF GENERALIZED FUNCTIONS IN PLANE BOUNDARY VALUE PROBLEMS OF UNCOUPLED THERMOELASTODYNAMICS

2021 ◽  
Author(s):  
Assiyat Dadayeva ◽  
Lyudmila Alexeyeva
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Generalized Functions ◽  
Boundary Integral ◽  
Generalized Solutions ◽  
Plane Boundary ◽  
Unknown Boundary ◽  
Singular Boundary

Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.

scholarly journals Singular Boundary Integral Equations of Boundary Value Problems for Hyperbolic Equations of Mathematical Physics

2020 ◽  
Author(s):  
Lyudmila A. Alexeyeva ◽  
Gulmira K. Zakiryanova
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Hyperbolic Equations ◽  
Boundary Integral Equations ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Generalized Solution ◽  
Boundary Integral ◽  
Singular Boundary ◽  
Equations Of Mathematical Physics

The method of boundary integral equations is developed for solving the nonstationary boundary value problems (BVP) for strictly hyperbolic systems of second-order equations, which are characteristic for description of anisotropic media dynamics. The generalized functions method is used for the construction of their solutions in spaces of generalized vector functions of different dimensions. The Green tensors of these systems and new fundamental tensors, based on it, are obtained to construct the dynamic analogues of Gauss, Kirchhoff, and Green formulas. The generalized solution of BVP has been constructed, including shock waves. Using the properties of integrals kernels, the singular boundary integral equations are constructed which resolve BVP. The uniqueness of BVP solution has been proved.

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