Time-Dependent Plane Wave Diffraction by a Half-Plane: Explicit Solution for Rawlins' Mixed Initial Boundary Value Problem

1998 ◽  
Vol 78 (5) ◽  
pp. 321-334 ◽  
Author(s):  
Klaus Rottbrand
Keyword(s):  
Plane Wave ◽  
Boundary Value Problem ◽  
Half Plane ◽  
Wave Diffraction ◽  
Explicit Solution ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Time Dependent ◽  
Initial Boundary Value ◽  
Plane Wave Diffraction

On an initial boundary value problem involving Beltrami-Moses fields in electromagnetic theory

1993 ◽  
Vol 344 (1671) ◽  
pp. 235-248 ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Electromagnetic Theory ◽  
Time Dependent ◽  
Covariant Formulation ◽  
Beltrami Fields ◽  
Initial Boundary Value ◽  
Infinite Media

The so-called Harmuth ansatz consists of including autonomous magnetic sources in the time-dependent Maxwell postulates. The Beltrami fields are eigenfunctions of the curl operator, and have been used by Moses for propagation in infinite media. These developments are of relatively recent provenances in electromagnetic theory. We discuss an initial-boundary value problem (IBVP) within the framework of a manifestly covariant electromagnetic formalism by using the Harmuth ansatz. We also show how a covariant formulation of the Beltrami-Moses fields may be used for solving electromagnetic IBVPS.

scholarly journals EXPLICIT SOLUTION OF THE MIXED PROBLEM IN ANISOTROPIC SEMISPACE WITH BRIGHTLY EXPRESSED VERTICAL PERMEABILITY FOR BARENBLATT–ZHELTOV–KOCHINA EQUATION

2017 ◽  
Vol 18 (6) ◽  
pp. 75-99
Author(s):  
Kh.G. Umarov
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Mixed Problem ◽  
Explicit Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Porous Rocks ◽  
Vertical Permeability ◽  
Initial Boundary Value

For Barenblatt–Zheltov–Kochina model presentation of filtering of liquids in fissured-porous rocks the explicit solution of the mixed problem in anisotropic semispace with brightly expressed vertical permeability is found by reduction of the considered problem of filtering to the solution of the abstract initial boundary-value problem in Banach space.

scholarly journals Time-dependent Stokes equations with measure data

2003 ◽  
Vol 2003 (17) ◽  
pp. 953-973 ◽  
Author(s):  
Bui An Ton
Keyword(s):  
Boundary Value Problem ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Time Dependent ◽  
Measure Data ◽  
Cylindrical Domain ◽  
Data Feedback ◽  
Feedback Laws ◽  
Initial Boundary Value

We establish the existence of a unique solution of an initial boundary value problem for the nonstationary Stokes equations in a bounded fixed cylindrical domain with measure data. Feedback laws yield the source and its intensity from the partial measurements of the solution in a subdomain.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

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