Problems with Insufficient Information about Initial-boundary Data

2009 ◽  
pp. 349-378
Author(s):  
E. V. Radkevich
Keyword(s):  
Boundary Data ◽  
Initial Boundary ◽  
Insufficient Information

THE GREEN'S FUNCTION FOR THE BROADWELL MODEL WITH A TRANSONIC BOUNDARY

2008 ◽  
Vol 05 (02) ◽  
pp. 279-294 ◽  
Author(s):  
CHIU-YA LAN ◽  
HUEY-ER LIN ◽  
SHIH-HSIEN YU
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Green's Function ◽  
Boundary Data ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Convergent Series ◽  
Iteration Scheme ◽  
Initial Boundary Value

We study an initial boundary value problem for the Broadwell model with a transonic physical boundary. The Green's function for the initial boundary value problem is obtained by combining the estimates of the full boundary data and the Green's function for the initial value problem. The full boundary data is constructed from the imposed boundary data through an iteration scheme. The iteration scheme is designed to separate the interaction between the boundary wave and the interior wave and leads to a convergent series in the iterative boundary estimates.

scholarly journals Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130341 ◽  
Author(s):  
Elena I. Kaikina
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Boundary Data ◽  
Schrodinger Equation ◽  
Large Time ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Robin Boundary

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time.

Determination of Unknown Coefficients in Parabolic Operators from Overspecified Initial-Boundary Data

1978 ◽  
Vol 100 (3) ◽  
pp. 503-507 ◽  
Author(s):  
J. R. Cannon ◽  
P. C. DuChateau
Keyword(s):  
Boundary Value Problems ◽  
Boundary Data ◽  
Boundary Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Asymptotic Boundary ◽  
Nonlinear Parabolic ◽  
Determination Of Parameters ◽  
Initial Boundary Value

Application of some asymptotic boundary behavior results for solutions of nonlinear parabolic initial boundary value problems is made to the determination of unknown coefficients and parameters in parabolic operators from overspecified boundary data. Some numerical results on the determination of parameters is presented and discussed.

Non-equilibrium imbibition of a porous block

1996 ◽  
Vol 7 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Arkady Gilman
Keyword(s):  
Initial Data ◽  
Boundary Data ◽  
Initial Boundary ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Boundary Problems ◽  
The Maximum Principle ◽  
Image Position ◽  
Well Posed ◽  
Non Equilibrium

We consider a phenomenological model proposed by Barenblatt [1] for non-equilibrium two-phase flow in porous media. In the case of zero total flow it reduces to a pair of equations:where Φ(σ) is a non-decreasing (not necessarily increasing) smooth function defined in the interval 0 ≤ σ ≤ 1. We consider initial-boundary problems for this system in which the initial data are given only for s, and the boundary data only for ς (which corresponds to the physical sense of the model). The degenerate character of the system allows us to apply simple topological methods. We show that the boundary problem is well-posed, in the sense that there exits a unique (weak) solution which satisfies the maximum principle and depends continuously on the initial data. The solution is no less smooth than the initial and boundary data.

scholarly journals Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

2009 ◽  
Vol 465 (2111) ◽  
pp. 3341-3360 ◽  
Author(s):  
Guillaume Michel Dujardin
Keyword(s):  
Schrödinger Equation ◽  
Asymptotic Behaviour ◽  
Boundary Value Problems ◽  
Boundary Data ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Half Line ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas’ transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over π .

A bounded and monotone finite-difference solution of a hyperbolic Burgers–Fisher equation

2018 ◽  
Vol 29 (12) ◽  
pp. 1850122
Author(s):  
L. A. Flores-Oropeza ◽  
A. Román-Loera ◽  
Ahmed S. Hendy
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Traveling Wave ◽  
Boundary Data ◽  
Traveling Wave Solutions ◽  
Initial Boundary ◽  
Fisher Equation ◽  
Wave Solutions ◽  
Nonlinear Advection ◽  
Finite Difference Solution

In this work, a nonlinear finite-difference scheme is provided to approximate the solutions of a hyperbolic generalization of the Burgers–Fisher equation from population dynamics. The model under study is a partial differential equation with nonlinear advection, reaction and damping terms. The existence of some traveling-wave solutions for this model has been established in the literature. In the present manuscript, we investigate the capability of our technique to preserve some of the most important features of those solutions, namely, the positivity, the boundedness and the monotonicity. The finite-difference approach followed in this work employs the exact solutions to prescribe the initial-boundary data. In addition to providing good approximations to the analytical solutions, our simulations suggest that the method is also capable of preserving the mathematical features of interest.

The Global Solution of Viscoelastic Thin Rectangular Plate Equation

2010 ◽  
Vol 29-32 ◽  
pp. 577-582
Author(s):  
Dan Xia Wang ◽  
Jian Wen Zhang
Keyword(s):  
Rectangular Plate ◽  
Existence And Uniqueness ◽  
Boundary Data ◽  
Initial Boundary ◽  
Viscoelastic Plate ◽  
Plate Equation ◽  
Thin Rectangular Plate ◽  
Global Strong Solution ◽  
Nonlinear Viscoelastic ◽  
Priori Estimates

In this paper, we consider a class of nonlinear viscoelastic plate equation with strong damping which arises from the model of the viscoelastic thin rectangular plate with four edges supported. By virtue of Faedo-Galerkin method combined with the priori estimates, we prove the existence and uniqueness of the global strong solution under certain initial-boundary data for the above-mentioned equation.

3-D flow of a compressible viscous micropolar fluid model with spherical symmetry: A brief survey and recent progress

2018 ◽  
Vol 30 (01) ◽  
pp. 1830001 ◽  
Author(s):  
Ivan Dražić
Keyword(s):  
Spherical Symmetry ◽  
Micropolar Fluid ◽  
Boundary Data ◽  
Fluid Model ◽  
Initial Density ◽  
Initial Boundary ◽  
Generalized Solution ◽  
Heat Conducting ◽  
Initial Boundary Problem ◽  
Concentric Spheres

We consider the non-stationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid with the assumption of spherical symmetry. We analyze the flow between two concentric spheres that present solid thermo-insulated walls. The fluid is perfect and polytropic in the thermodynamical sense and the initial density and temperature are strictly positive. The corresponding problem has homogeneous boundary data. In this work, we present the described model and provide a brief overview of the progress in the mathematical analysis of the associated initial-boundary problem. We consider existence and uniqueness of the generalized solution, asymptotic behavior of the solution and regularity of the solution.

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