Construction of a new source function for the parabolic equation algorithm

1977 ◽  
Vol 61 (S1) ◽  
pp. S12-S12
Author(s):  
H. M. Garon ◽  
J. S. Hanna ◽  
P. V. Rost
Keyword(s):  
Parabolic Equation ◽  
Source Function

scholarly journals The Problem of Determining of the Source Function and of the Leading Coefficient in the Many-dimensional Semilinear Parabolic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 497-506
Author(s):  
Svetlana V. Polyntseva ◽  
◽  
Kira I. Spirina
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Source Function ◽  
Time Interval ◽  
Semilinear Parabolic Equation ◽  
Existence And Uniqueness Theorem ◽  
Bounded Functions ◽  
The Many ◽  
Semilinear Parabolic

We consider the problem of determining the source function and the leading coefficient in a multidimensional semilinear parabolic equation with overdetermination conditions given on two different hypersurfaces. The existence and uniqueness theorem for the classical solution of the inverse problem in the class of smooth bounded functions is proved. A condition is found for the dependence of the upper bound of the time interval, in which there is a unique solution to the inverse problem, on the input data

COMPUTING THE INFLUENCE OF DOPPLER DUE TO SOURCE/RECEIVER MOTION IN A PARABOLIC EQUATION MODEL

2002 ◽  
Vol 10 (03) ◽  
pp. 295-309
Author(s):  
KEVIN B. SMITH
Keyword(s):  
Parabolic Equation ◽  
Numerical Method ◽  
Source Function ◽  
Amplitude Spectrum ◽  
Vertical Plane ◽  
Equation Model ◽  
Post Processing ◽  
Platform Motion ◽  
Wavenumber Domain ◽  
Source Motion

A numerical method for computing the influence of Doppler due to source/receiver platform motion in a parabolic equation model is introduced. Both source/receiver speeds and angles of motion in the vertical plane are included in the specification of the motion. By necessity, it is shown that the source function must be defined in the vertical wavenumber domain. Furthermore, the source amplitude spectrum must be defined prior to the calculation, in contrast to previous implementations which would allow for application of variable spectra in post-processing. Examples are given for simple environments demonstrating the expected influence of Doppler due to source motion.

scholarly journals On the existence and uniqueness of the solution of the coefficient inverse problem for a semilinear parabolic equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012008
Author(s):  
A L Sugezhik
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Source Function ◽  
Semilinear Parabolic Equation ◽  
Coefficient Inverse Problem ◽  
Uniqueness Of The Solution ◽  
Bounded Functions ◽  
Semilinear Parabolic

Abstract In this paper, we consider the problem of determining the source function and the coefficient by the derivative with respect to time in a semilinear parabolic equation with overdetermination conditions defined on two different hyperplanes. The existence and uniqueness theorems of the classical solution of the posed coefficient inverse problem in the class of smooth bounded functions were proved. An example of input data satisfying the conditions of the proved theorems is given.

scholarly journals Inverse Problem for Source Function in Parabolic Equation at Neumann Boundary Conditions

2001 ◽  
Vol 14 (4) ◽  
pp. 445-451
Author(s):  
Victor K. Andreev ◽  
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Source Function ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Integral Overdetermination Condition ◽  
Integral Overdetermination ◽  
Initial Boundary Value ◽  
Problem Data

The second initial-boundary value problem for a parabolic equation is under study. The term in the source function, depending only on time, is to be unknown. It is shown that in contrast to the standard Neumann problem, for the inverse problem with integral overdetermination condition the convergence of it nonstationary solution to the corresponding stationary one is possible for natural restrictions on the input problem data

scholarly journals On some perturbation techniques for quasi-linear parabolic equations

1990 ◽  
Vol 3 (3) ◽  
pp. 169-175
Author(s):  
Igor Malyshev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Source Function ◽  
Nonlinear Boundary ◽  
Nonlinear Operator ◽  
Nonlinear Operator Equation ◽  
Linear Parabolic Equation ◽  
Perturbation Techniques ◽  
Linear Parabolic Equations

We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

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