Results 231 to 240 of about 13,776,135 (277)

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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Solving initial–boundary-value creep problems

International Applied Mechanics, 2009
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Morachkovskii, O. K., Romashov, Yu. V.
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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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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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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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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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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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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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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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