Fixed points of a destabilized Kuramoto-Sivashinsky equation

• We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension u(t) + nu u(xxx) + beta u(xx) + gamma uu(x) - alpha u for alpha, nu >= 0 and beta, gamma is an element of R. For certain parameter values, shock like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self consistent bounds and validated numerics. Published by Elsevier Inc.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Kuramoto-Sivashinsky equations

Boundary value problem

Galerkin projection

Self consistent bounds

Rigorous computations

Interval arithmetic

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