Inverse Logarithmic Potential Problem

V. G. Chedrednichenko (Autor)

Buch | Hardcover

254 Seiten

1996
VSP International Science Publishers (Verlag)
978-90-6764-202-6 (ISBN)

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This work deals with the solvability of the inverse potential problem in the two-dimensional case. A new method based on the theory of boundary-value problems for analytic functions and univalent functions is constructed, and a priori estimates and a parameter continuation method are established.

Part 1 Formulation of inverse logarithmic potential problem - fundamental equation: formulation of inverse problem; nonlinear boundary value problem for mapping function; the analytic continuation of the potential across a boundary; the boundary analyticity of domain is a solution to an inverse problem; the structure of inverse problem solution, final solvability, examples. Part 2 Local solvability of an inverse problem: univalent function variation; local theorem of existence; linearization of the boundary value problem; the auxiliary problem; the Newton-Kantorovitch method; the explicit solution of the linear problem; the local uniqueness theorem; the density variation - the equivalent solution set of the inverse problems - remarks; the complex-valued density case; existence theorems for the inverse problems for small constant densities; proof of theorems. Part 3 The estimate of bounded univalent function co-efficients and univalent polynomials. Part 4 Mass potential estimates - necessary conditions of solvability - a priori estimates for inverse problem solution. Part 5 The continuation by the parameter of an inverse problem solution. Part 6 On the analyticity and smoothness of an inverse problem solution. Part 7 Inverse linear problem - determination of a density of the given domain by its exterior potential. Part 8 Conjugation of harmonic and analytic functions - direct and inverse problems. Part 9 Applications in gravity prospecting and in magnetic prospecting. (Part contents)

Erscheint lt. Verlag	1.2.1996
Reihe/Serie	Inverse and Ill-Posed Problems Series
Verlagsort	Zeist
Sprache	englisch
Gewicht	560 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Geowissenschaften ► Geophysik
ISBN-10	90-6764-202-9 / 9067642029
ISBN-13	978-90-6764-202-6 / 9789067642026
Zustand	Neuware