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This project aims at comparing nonlinear evolution equations for premixed flames in large scale burners , where hydrodynamic effects are important, called self turbulent flames, to experiments. This type of flames is expected to have more applications in the next few years, as they have a number of advantages in terms of pollution reduction. However these flames are poorly understood. Building on recently developed experiments at the IRPHE laboratory that make use of a new device to damp acoustics and confirm the possibility of observing the propagation of wide flames through quiescent gases, we propose to experimentally study flames in simple situations such as a Hele-Shaw burner and test the predictions of theoretical models. The theoretical aspects will be developed in collaboration with G. Joulin (Pprime Institute), whose analytical works are a reference in the field. A better understanding of the coupling between turbulence and hydrodynamic instability of premixed flames is expected from this proposal. The study of flames in the Hele-Shaw burner will allow very precise experiments, leading to quasi two dimensional flames, which will be easy to study by image analysis. The results will be compared to theoretical and numerical studies of the Sivashinsky equation, the well-known model equation describing the non linear dynamics of premixed flames. We will study the statistical properties of flames in Hele Shaw cells, such as the probability density function of cells lengths or the fractal properties of the front. Analytical studies of the Sivashinsky equation will be performed, first in the case of a flame submitted to a stationary shear flow (where analytical solutions do not exist at the moment), then in the non stationary case. The study will be extended to very unstable flames submitted to an incident turbulence, with predictions of the turbulent flame velocity versus turbulence intensity. These predictions will be compared to experiments.