Click Volume Potential Maximization in Affiliate Network

On spectral and boundary properties of the volume potential for the Helmholtz equation

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2019001 ◽

2019 ◽

Vol 14 (5) ◽

pp. 502

Author(s):

Tynysbek Sharipovich Kalmenov ◽

Michael Ruzhansky ◽

Durvudkhan Suragan

Keyword(s):

Helmholtz Equation ◽

Differential Operators ◽

Nonlocal Boundary ◽

Spectral Geometry ◽

Bessel Potential ◽

Nonlocal Boundary Value Problem ◽

Volume Potential ◽

Potential Operators ◽

Boundary Properties ◽

Krahn Inequality

In this paper, we study boundary properties and some questions of spectral geometry for certain volume potential type operators (Bessel potential operators) in an open bounded Euclidean domains. In particular, the results can be valid for differential operators, which are related to a nonlocal boundary value problem for the Helmholtz equation, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of the Rayleigh-Faber-Krahn inequality.

Download Full-text

Second derivatives of the volume potential and integral equations in electrodynamics

Computational Mathematics and Modeling ◽

10.1007/s10598-012-9128-z ◽

2012 ◽

Vol 23 (2) ◽

pp. 168-174

Author(s):

V. I. Dmitriev

Keyword(s):

Integral Equations ◽

Volume Potential ◽

Second Derivatives ◽

Derivatives Of

Download Full-text

Renal regulation of urine volume: potential implications for nocturia

BJU International ◽

10.1046/j.1464-410x.90.s3.2.x ◽

2002 ◽

Vol 90 ◽

pp. 7-10 ◽

Cited By ~ 25

Author(s):

G.L. Robertson ◽

J.P. Norgaard

Keyword(s):

Urine Volume ◽

Volume Potential

Download Full-text

THE VALUE OF THE SOLUTION OF ONE PROBLEM FOR THE PSEUDOPARABOLIC EQUATION IN THE CLASS OF GELS

Bulletin Series of Physics & Mathematical Sciences ◽

10.51889/2020-2.1728-7901.11 ◽

2020 ◽

Vol 70 (2) ◽

pp. 77-83

Author(s):

U.K. Koylyshov ◽

◽

A.Zh. Aldashova ◽

Keyword(s):

Cauchy Problem ◽

Parabolic Equation ◽

Fundamental Solution ◽

A Priori Estimates ◽

Dimensional Space ◽

Three Dimensional ◽

Initial Condition ◽

Pseudoparabolic Equation ◽

Volume Potential ◽

The Cauchy Problem

This article discusses the Cauchy problem for a pseudo-parabolic equation in three-dimensional space. The result can be generalized to - dimensional space. The Cauchy problem for equations of parabolic and elliptic types is well studied. For a pseudo-parabolic equation using the previously constructed fundamental solution, evaluating the fundamental solution and its derivatives. Applying the Fourier transform with respect to and the Laplace transform with, we first obtained a priori estimates for the potentials of the initial condition and the volume potential in Hölder spaces. Further, using these results, we have proved an estimate of the solution of the Cauchy problem for the pseudo-parabolic equation in Hölder classes. A detailed proof of the estimation of the potentials of the initial condition, the volume potential, and the solution of the Cauchy problem for the pseudoparabolic equation is given

Download Full-text