Results 231 to 240 of about 1,212,620 (281)

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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Some initial-boundary value problems

2016
In this chapter we will study initial-boundary value problems and their treatment by methods of quaternionic analysis in combination with classical analytic numerical techniques. We start with a brief discussion of strategies for the treatment of time-dependent parabolic problems. Three methods should be considered here: the horizontal method of lines,
Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig   +2 more
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Nonlinear initial-boundary value problems

Nonlinear Analysis: Theory, Methods & Applications, 1987
We prove global existence, uniqueness and exponential decay of a global solution, u(t), of a Cauchy problem in a Hilbert space H for an equation whose weak formulation is \[ \frac{d}{dt}(u',v)+\delta (u',v)+\alpha b(u,v)+\beta a(u,v)+(G(u),v)=0 \] where \('=d/dt\), (,) is the inner product in H, b(u,v), a(u,v) are given forms on subspaces \(U\subset W\)
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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 Random Initial Boundary Value Problem

1992
When dealing with Problems 1 and 2 introduced in Section 2 of Chapter 1, the physical situation to be studied can be considered as an input-output system where the set of initial and boundary conditions represent the input and the actual solution of the problem is the output and the phenomenology is modelled by a partial differential equation.
N. Bellomo, Z. Brzezniak, L. M. de Socio
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Deferred Correction Methods for Initial Boundary Value Problems

Journal of Scientific Computing, 2002
The numerical solution of the linear problem \[ {\partial u\over\partial t}={\mathcal P}(u)+ F(x,t),\quad u(x,0)= f(x) \] with appropriate boundary conditions by the method of lines gives rise to a large system of ordinary differential equations.
Kress, Wendy, Gustafsson, Bertil
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VARIABLE-COEFFICIENTS INITIAL BOUNDARY VALUE PROBLEMS

2006
Abstract This chapter turns to linear IBVPs with variable coefficients. The techniques mix those of Chapters 2 and 4. Dissipative boundary symmetrizers have now variable coefficients, and are viewed as symbolic symmetrizers, from which the chapter builds functional dissipative symmetrizers.
Sylvie Benzoni-Gavage, Denis Serre
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Initial-Boundary Value and LC Problems

2013
Evaluation of European-style derivatives can be reduced to solving initial value or initial-boundary value problems of parabolic partial differential equations. This chapter discusses numerical methods for such problems. If an American option problem is formulated as a linear complementarity problem, then the only difference between solving a European ...
You-lan Zhu, Xiaonan Wu, I-Liang Chern, Zhi-zhong Sun   +3 more
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Application to semilinear initial-boundary value problems

1991
This chapter is devoted to the semigroup approach to a class of initialboundary value problems for semilinear parabolic differential equations. We prove Theorem 1.5 by using the theory of fractional powers of analytic semigroups (Theorems 10.1 and 10.2). To do this, we verify that all the conditions of Theorem 2.8 are satisfied.
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One-dimensional initial-boundary value problems

2003
We known from experiments that deformation of a body under drying is associated with a change of moisture content and temperature of the body. The motion of a saturated porous solid under drying, described by velocity vs (see Section 3.1). is characterized by mutual interaction between deformation, moisture content and temperature fields. The domain of
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