A modified quasi-boundary value method for regularizing of a backward problem with time-dependent coefficient

2011 ◽  
Vol 19 (3) ◽  
pp. 409-423 ◽  
Author(s):  
Pham Hoang Quan ◽  
Dang Duc Trong ◽  
Le Minh Triet ◽  
Nguyen Huy Tuan
Keyword(s):  
Boundary Value ◽  
Time Dependent ◽  
Backward Problem ◽  
Boundary Value Method

scholarly journals A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Pham Hoang Quan ◽  
Le Minh Triet ◽  
Dang Duc Trong
Keyword(s):  
Exact Solution ◽  
Parabolic Equation ◽  
Numerical Experiment ◽  
Time Dependent ◽  
Backward Problem ◽  
Nonlinear Parabolic ◽  
Boundary Value Method ◽  
Ill Posed ◽  
Sharp Error ◽  
Regularized Solution

We study the backward problem with time-dependent coefficient which is a severely ill-posed problem. We regularize this problem by combining quasi-boundary value method and quasi-reversibility method and then obtain sharp error estimate between the exact solution and the regularized solution. A numerical experiment is given in order to illustrate our results.

Error control Gaussian collocation software for boundary value ODEs and 1D time-dependent PDEs

2019 ◽  
Vol 81 (4) ◽  
pp. 1505-1519
Author(s):  
Mark Adams ◽  
Connor Tannahill ◽  
Paul Muir
Keyword(s):  
Error Control ◽  
Boundary Value ◽  
Time Dependent

Beam Vibrations With Time-Dependent Boundary Conditions

1950 ◽  
Vol 17 (4) ◽  
pp. 377-380
Author(s):  
R. D. Mindlin ◽  
L. E. Goodman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Time Dependent ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Vibration Problems

Abstract A procedure is described for extending the method of separation of variables to the solution of beam-vibration problems with time-dependent boundary conditions. The procedure is applicable to a wide variety of time-dependent boundary-value problems in systems governed by linear partial differential equations.

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.

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