Mathematics
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Item Stability analysis of finite-difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems(Copyright: Society for Industrial and Applied Mathematics, 1987-12) Tadmor, EitanItem Stability analysis of spectral methods for hyperbolic initial-boundary value systems(Copyright: Society for Industrial and Applied Mathematics, 1987-04) Gottlieb, David; Lustman, Liviu; Tadmor, EitanItem Convergence of spectral methods for hyperbolic initial-boundary value systems(Copyright: Society for Industrial and Applied Mathematics, 1987-06) Gottlieb, David; Lustman, Liviu; Tadmor, EitanItem Convergence of spectral methods for hyperbolic initial-boundary value systems(Copyright: Society for Industrial and Applied Mathematics, 1987-06) Gottlieb, David; Lustman, Liviu; Tadmor, EitanItem THE WELL-POSEDNESS OF THE KURAMOTO-SIVASHINSKY EQUATION(copyright: Society for Industrial and Applied Mathematics, 1986-07) Tadmor, EitanThe Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction-diffusion systems, flame-propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of quadratic nonlinearity and arbitrary linear parabolic part. We show that such equations are well-posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by "patching" in the large short time solutions without "loss of derivatives".