Results 311 to 320 of about 1,451,898 (379)

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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Inhomogeneous initial-boundary value problem for the 2Dnonlinear Schrödinger equation

Journal of Mathematics and Physics, 2018
We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear multidimensional Schrodinger equation, formulated on an upper right-quarter plane.
E. Kaikina
semanticscholar   +1 more source

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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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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