### Quasi-linear equations in Bbb R^N perturbation results

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This is joint work with S. In this talk we shall present recent results, obtained in collaboration with J.

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Castellanos and G. Petronilho, concerning the analytic resp.

Gevrey regularity of analytic resp. Gevrey vectors associated to system of vector fields defined by locally integrable tube structures. We shall also explain how these results can be applied to the study of regularity of solutions to certain systems of semi-linear PDE. We are interested in the existence of microlocal subelliptic estimates for some systems of complex vector fields which are special classes of locally integrable systems.

In the case of codimension 1, the situation is quite clear: the necessary condition of F. Treves for microlocal hypoellipticity, he gave in the seventies, is also sufficient in case the coefficients are analytic,by a result of H Maire. Maire gave also an example showing that this is not the case for higher codimension systems. So we study also some classes of vector fields, even in higher codimension case, for which we obtain microlocal suellipticity and also maximal estimates hence microlocal hypoellipticity, for these systems and the associated second order operators. This is a joint work with Bernard Helffer.

## Marrakesh workshop, May 10-14, 2010

Transversality is an important notion in geometry. We shall consider transversality in the context of mappings between generic submanifolds in complex space. We will present some new results that extend previous results and answers questions posed by the speaker and Linda Rothschild some five years ago. This joint work with Son Doung. In the analytic case, i.

### 1st Edition

Eakin and A. In this talk we prove that the same statement does not hold for a quasianalytic system unless this system is analytic. By considering a nonlinear eigenvalue problem the existence and stability of the selfsimilar profiles is discussed. View on Royal Society. Open Access.

Save to Library. Create Alert. Share This Paper. Citations Publications citing this paper. On global solutions and blow-up for Kuramoto—Sivashinsky-type models, and well-posed Burnett equations Victor A. Galaktionov , Enzo Mitidieri , Stanislav I. Three tupes of self-similar blow-up for the fourth-order p-Laplacian equaiton with source: variational and branching approaches Victor A. Three types of self-similar blow-up for the fourth-order p-Laplacian equation with source Victor A.

Akhmet, Mathematical Review: MR m Akhmet, C.

Akhmet, Mathematical Review: MR b Tleubergenova, O. Akhmet, Almost periodic solutions of differential equations with piecewise constant argument of generalized type. Akhmet, Asymptotic behavior of solutions of differential equations with piecewise constant arguments.

## TMNA - Volume 37 Number 1

Akhmet, Hyperbolic sets of impact systems. Discrete Impuls. A Math. Akhmet, Devaney's chaos of a relay system. Akhmet, J. Alzabut, A. Zafer, On periodic solutions of linear impulsive delay differential systems. Akhmet, D. Arugaslan and X. Akhmet, Stability of differential equations with piecewise constant arguments of generalized type. Akhmet, The complex dynamics of the cardiiovascular system. Turan, Differential equations on variable time-scales. U, Preface. Akhmet, Creating a chaos in a system with relay.

Akhmet, E. Yilmaz, Hopfield-type neural networks systems with piecewise constant argument. Nonlinear Sci. Akhmet, Almost periodic solutions of the linear differential equations with piecewise constant argument..