12 citations · 12 across the 5 of their papers we have counts for
6 papers
On the Necessity of Logarithmic Estimates for Hypoellipticity
Timur Akhunov, Lyudmila Korobenko
This paper is focused on necessary conditions for hypoellipticity of an operator of the form , where the operator is either elliptic or parabolic, $L…
Necessity of a logarithmic estimate for hypoellipticity of some degenerately elliptic operators
Timur Akhunov, Lyudmila Korobenko
This paper extends a class of degenerate elliptic operators for which hypoellipticity requires more than a logarithmic gain of derivatives of a solution in every direction. Work of…
Well-posedness of fully nonlinear KdV-type evolution equations
Timur Akhunov, David M. Ambrose, J. Douglas Wright
We study the well-posedness of the initial value problem for fully nonlinear evolution equations, where may depend on up to the first three spatial derivatives of…
Hypoellipticity without loss of derivatives for Fedii's type operators
Timur Akhunov, Lyudmila Korobenko, Cristian Rios
We prove that second order linear operators on of the form , where and satisfy Morimoto's super-logari…
A sharp condition for the well-posedness of the linear KdV-type equation
Timur Akhunov
To make the illposedness argument more transparent the argument is rewritten to reduce the equation to the constant dispersion case. Minor errors are corrected. Accepted to the Pro…
Local Well Posedness of Quasi-Linear Systems Generalizing KdV
Timur Akhunov
In this article we prove local well-posedness of quasilinear dispersive systems of PDE generalizing KdV. These results adapt the ideas of Kenig- Ponce-Vega from the Quasi-Linear Sc…