### A blow-up mechanism for a chemotaxis model

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Let $P$ be a linear partial differential operator with analytic coefficients. We assume that $P$ is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let $q$ be a characteristic point for $P$. We assume that $q$ lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that $P$ is analytic hypoelliptic at $q$. Hence Okaji has established the validity of Treves’ conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of...

In this talk we extend to Gevrey-s obstacles with $1\le s\<3$ a result on the poles free zone due to J. Sjöstrand [8] for the analytic case.

We prove that any elliptic operator of second order in variational form is the infinitesimal generator of an analytic semigroup in the functional space ${C}^{-1,\alpha}(\mathrm{\Omega})$ consinsting of all derivatives of hölder-continuous functions in $\mathrm{\Omega}$ where $\mathrm{\Omega}$ is a domain in ${\mathbb{R}}^{n}$ not necessarily bounded. We characterize, moreover the domain of the operator and the interpolation spaces between this and the space ${C}^{-1,\alpha}(\mathrm{\Omega})$. We prove also that the spaces ${C}^{-1,\alpha}(\mathrm{\Omega})$ can be considered as extrapolation spaces relative to suitable non-variational operators....

The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.