Hypersingular Integral Equations and Their Applications (Electronic book text)

Hypersingular Integral Equations and Their Applications presents various methods for solving singular and hypersingular integral equations. In particular, the authors construct new exact analytical solutions of some two-dimensional hypersingular integral equations and obtain an analytical solution in quadratures for the hypersingular equation on the sphere. They present theorems for the existence and uniqueness of solutions for hypersingular integral equations, and the theory they develop in this monograph can be used to investigate the convergence of approximate solutions obtained by finite-difference methods for elliptic-type partial differential equations.Numerous examples demonstrate some of the many applications of hypersingular integral equations. These include solutions to problems involving flow past the deck of a ship, the diffraction of acoustic waves on a cube, and flow past an airfoil with suction on its surface.About the authors: Ivan K.; Lifanov is Head of the Department of Mathematics at the Zhukovsky Air Force Engineering Academy and a Chief Researcher at the Institute of Computing Mathematics at the Russian Academy of Sciences, and a Professor at Orel State University. His research interests focus on numerical methods, integral equations, and aerodynamics.Lev Poltavskii is a Professor in the Department of Mathematics at the Zhukovsky Air Force Engineering Academy and author of more than 50 scientific publications.G.M. Vainikko is a Professor at the Helsinki University of Technology. His research interests lie in applied mathematics, differential and integral equations, ill-posed problems, and inverse problems