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On the initial boundary value problem for Temple systems
Nonlinear Analysis: Theory, Methods & Applications, 2004The 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.
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On a hyperbolic perturbation of a parabolic initial–boundary value problem
Applied Mathematics Letters, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Soliton generation for initial-boundary-value problems
Physical Review Letters, 1992Summary: 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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MHD instabilities as an initial boundary-value problem
Nuclear Fusion, 1974The 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
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On the initial-boundary value problems for soliton equations
Journal of Experimental and Theoretical Physics Letters, 2001We present a novel approach to solving initial-boundary value problems on the segment and the half line for soliton equations. Our method is illustrated by solving a prototypal and widely applied dispersive soliton equation—the celebrated nonlinear Schroedinger equation. It is well known that the basic difficulty associated with boundaries is that some
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