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Linear Stability of Schwarzschild-Anti-de Sitter Spacetimes III: Quasimodes and Sharp Decay of Gravitational Perturbations. [PDF]

Commun Math Phys
Graf O, Holzegel G.
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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
exaly   +4 more sources

On a hyperbolic perturbation of a parabolic initial–boundary value problem

Applied Mathematics Letters, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexander A Zlotnik
exaly   +3 more sources

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, A. S., Its, A. R.
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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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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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