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Global dissipativity and inertial manifolds for diffusive burgers equations with low-wavenumber instability

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  • The global well-posedness, the existence of globally absorbing sets and the existence of inertial manifolds are investigated in a class of diffusive (viscous) Burgers equations. The class includes diffusive Burgers equation with nontrivial forcing, Burgers-Sivashinsky equation and Quasi-Steady equation of cellular flames. Global dissipativity is proven in two space dimensions for periodic boundary conditions. For the proof of the existence of inertial manifolds, the spectral-gap condition, which Burgers-type equations do not satisfy in their original form, is circumvented by employing the Cole-Hopf transform. The procedure is valid in both one and two space dimensions.
    Mathematics Subject Classification: 35K55, 35B41, 35B42, 37L25.


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