Results 231 to 240 of about 13,776,135 (276)

The Initial-Boundary Value Problem

2004
In this chapter, we extend the analysis of Chapter 7 and consider the evolution of the scalar initial-boundary value problem (6.16)–(6.20), namely, $$ u_t = u_{xx} + f(u), x,t > 0, $$ (1) $$ f(u) = \left\{ {\begin{array}{*{20}c} {(1 - u)u^m - ku^n ,u > 0,} \\ {0, u \leqslant 0,} \\ \end{array} } \right. $$ (2) $$ u(x,0) = \left\{
J. A. Leach, D. J. Needham
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MHD instabilities as an initial boundary-value problem

Nuclear Fusion, 1974
The gross MHD instabilities of straight cylindrical plasmas with elongated cross-section are investigated by solving the linearized MHD equations as an initial boundary-value problem on the computer. The linearized equations are Fourier-analysed along the ignorable co-ordinate of the equilibrium in order to reduce the computation to two dimensions. The
Bateman, G., Schneider, W., Grossmann, W.   +2 more
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The Initial-Boundary Value Problem and the Constraint

2013
In this chapter we introduce the definitions of boundary data and of constraints. More precisely, we study the initial-boundary value problem in Sect. 6.2, the constrained Riemann problem in Sect. 6.3, the constrained Cauchy problem in Sect. 6.4 and finally the constrained initial-boundary value problem in the last section.
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On the initial-boundary value problems for soliton equations

Journal of Experimental and Theoretical Physics Letters, 2001
We present a novel approach to solving initial-boundary value problems on the segment and the half line for soliton equations. Our method is illustrated by solving a prototypal and widely applied dispersive soliton equation—the celebrated nonlinear Schroedinger equation. It is well known that the basic difficulty associated with boundaries is that some
DE GASPERIS, Antonio, S. V. MANAKOV, SANTINI, Paolo Maria   +2 more
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Initial Value and Boundary Value Problems

2011
The energy balance models by Sellers (1969) and Budyko (1969) result in a linear partial differential equation of 1st order in time and 2nd order in space, (4.9).
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Solving initial–boundary-value creep problems

International Applied Mechanics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Morachkovskii, O. K., Romashov, Yu. V.
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Transformation of a Boundary Value Problem to an Initial Value Problem

1985
The method for transforming nonlinear boundary value problems to initial value problems was first introduced by Toepfer1 in 1912 in his attempt to solve Blasius’ equation in boundary layer theory by a series expansion method. About half a century later Klamkin2, based on the same reasoning, extended the method to a wider class of problems.
R. Seshadri, T. Y. Na
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Initial Boundary Value Problem for Conservation Laws

Communications in Mathematical Physics, 1997
Initial boundary value problems for systems of quasilinear hyperbolic conservation laws are studied. The main assumption is that the system admits a convex entropy extension. Then any twice differentiable entropy fluxes have traces on the boundary if the bounded solutions are generated by either Godunov schemes, or by suitable viscous approximations ...
Kan, Pui Tak, Santos, Marcelo M., Xin, Zhouping   +2 more
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BOUNDARY AND INITIAL VALUE PROBLEMS AND INTEGRAL OPERATOR

Advances in Differential Equations and Control Processes, 2018
Summary: In this paper, we consider an initial value problem of integrodifferential type (IVP). This kind of problem transforms into Fredholm-Volterra integral equation of second kind (F-VIESK). We discuss the existence of a unique solution of the problem by using Banach fixed point theorem.
Alharbi, F. M., Abdou, M. A.
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Initial Value Problem for Boundary Values of a Green’s Function

SIAM Journal on Applied Mathematics, 1974
An initial value problem for the boundary values of the Green’s function associated with a two-point boundary value problem is formulated. The applications to wave propagation problems, both of the deterministic and stochastic kind are discussed.
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