Results 261 to 270 of about 151,098 (306)

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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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.
Wendy Kress, Bertil Gustafsson
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Abstract initial boundary value problems

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1994
We consider abstract initial boundary value problems in a spirit similar to that of the classical theory of linear semigroups. We assume that the solution u at time t is given by u(t) = S(t) ξ + V(t)g, where ξ and g are respectively the initial and boundary data and S(t) and V(t) are linear operators.
Palencia, C., Alonso Mallo, I.
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The Initial-Boundary-Value Problems in the Theory of Micropolar Fluids

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1978
AbstractThe author considers the existence of solutions of the initial‐boundary‐value problem for the equations which describe the flow of incompressible micropolar fluids, by using a related, simpler set of equations and then taking a limit.
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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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On the numerical study of nonlinear initial-boundary value problems or initial-value problems

Applied Mathematics and Computation, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zaki F. A. El-Reheem, A. H. Nasser
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Initial-boundary value problems on the sphere

2016
In this chapter, we consider classes of fluid flow problems on the sphere and in ball shells with given initial and boundary value conditions. We focus our attention on the corresponding Navier-Stokes equations and their linearizations – the socalled forecasting equations.
Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig   +2 more
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On the initial boundary value problem for a shallow water equation

Journal of Mathematical Physics, 2004
In this paper, we obtain the existence and uniqueness of the local strong solutions to the initial boundary problem for a one-dimensional shallow-water equation (Camassa–Holm equation) on the half-space {x>0} with initial data uo∈H2(R+)∩H01(R+). The solution is obtained as a limit of the solutions for a class of approximation problems.
Ma, Shixiang, Ding, Shijin
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An initial boundary value problem of Camassa–Holm equation

Journal of Mathematical Physics, 2000
In this paper, the local existence and blow-up for an initial boundary value problem of the Camassa–Holm equation are obtained.
Kwek, K.-H., Gao, H., Zhang, W., Qu, C.
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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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