Results 231 to 240 of about 1,211,636 (285)

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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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

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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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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Initial-value methods for boundary-value problems

1987
As we saw in Chapter 1, a boundary-value problem is one in which conditions associated with the differential equations are specified at more than one point. Here we shall concentrate on the existence of just two boundary points, which is the most usual case.
L. Fox, D. F. Mayers
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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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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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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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