THE WELL-POSEDNESS OF THE KURAMOTO-SIVASHINSKY EQUATION
THE WELL-POSEDNESS OF THE KURAMOTO-SIVASHINSKY EQUATION
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Date
1986-07
Authors
Tadmor, Eitan
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Citation
E. Tadmor (1986). The well-posedness of the Kuramoto-Sivashinsky equation. SIAM Journal on Mathematical Analysis 17 (1986), 884-893.
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Abstract
The 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".