Results 311 to 320 of about 1,422,735 (373)

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.
C. Palencia, I. Alonso Mallo
openaire   +3 more sources

On the initial boundary value problem for Temple systems

Nonlinear Analysis: Theory, Methods & Applications, 2004
The hyperbolic system \(u_t +f(u)_x =0\) is considered in the domain \(t>0\), \(x>\Psi (t)\). Assumptions on the flux \(f: \mathbb R^n \to \mathbb R^n\) are imposed to state that the system is of the Temple type. The boundary condition \(u(t,\Psi (t))=\) \(\widetilde{u}(t)\) is satisfied in the Dubois-LeFloch sense [\textit{F.
COLOMBO, Rinaldo Mario, GROLI ALESSANDRO
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The initial-boundary value problem for the Schrödinger–Korteweg–de Vries system on the half-line

Communications in Contemporary Mathematics, 2019
We prove local well-posedness for the initial-boundary value problem (IBVP) associated to the Schrödinger–Korteweg–de Vries system on right and left half-lines.
M. Cavalcante, A. Corcho
semanticscholar   +1 more source

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

Soliton generation for initial-boundary-value problems

Physical Review Letters, 1992
Summary: The solution of the initial-boundary-value problem of integrabale nonlinear evolution equations, with the spatial variable on a half-infinite line, can be reduced to the solution of a linear intregral equation. The asymptotic analysis of this equation for large \(t\) shows how the boundary conditions can generate solitons.
Fokas As, Its Ar
openaire   +4 more sources

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\{
D. J. Needham, J. A. Leach
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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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The Random Initial Boundary Value Problem [PDF]

, 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.
Nicola Bellomo, L. M. de Socio, Z. Brzezniak   +2 more
openaire   +1 more source

Initial Boundary Value Problem for Conservation Laws [PDF]

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 ...
Marcelo M. Santos, Zhouping Xin, Pui Tak Kan   +2 more
openaire   +1 more source

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.
Wolfgang Sprößig, Klaus Gürlebeck, Klaus Habetha   +2 more
openaire   +2 more sources