Related papers: Exponentially long time stability for non--lineari…
We study finite Morse index solutions to the non-local Gelfand-Liouville problem $$ (-\Delta)^su=e^u\quad\mathrm{in}\quad \mathbb{R}^n,$$ for every $s\in(0,1)$ and $n>2s$. Precisely, we prove non-existence of finite Morse index solutions…
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
We investigate the three-dimensional (3D) incompressible anisotropic Navier-Stokes system with dissipation only in the horizontal variables, posed in a strip domain. To overcome the difficulties arising from the boundary terms and the…
We consider the Cauchy problem of the higher-order KdV-type equation: \[ \partial_t u + \frac{1}{\mathfrak{m}} |\partial_x|^{\mathfrak{m}-1} \partial_x u = \partial_x (u^{\mathfrak{m}}) \] where $\mathfrak{m} \ge 4$. The nonlinearity is…
In this paper, we prove the asymptotic stability of nonlinear Schrodiger equations on star graphs, which partially solves an open problem in D. Noja \cite{DN}. The essential ingredient of our proof is the dispersive estimate for the…
Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg-de Vries equation posed on a finite interval $\left[0, 2\pi \sqrt{7/3}\right]$. The equation comes with a Dirichlet boundary condition at…
Let $x=t^n$, $y=\sum_{i=1}^{\infty}a_it^i$ be a parametrisation of the germ of a complex plane analytic curve $\Gamma$ at the origin. Then $\Gamma$ has the implicit equation $f(x,y)=0$ in the neighbourhood of the origin, where $f=\sum…
We prove a sharp quantitative version of recent Faber-Krahn inequalities for the continuous Wavelet transforms associated to a certain family of Cauchy wavelet windows . Our results are uniform on the parameters of the family of Cauchy…
In this article we prove global propagation of analyticity in finite time for solutions of semilinear Schr\"odinger equations with analytic nonlinearity from a region $\omega$ where the Geometric Control Condition holds. Our approach…
We prove the existence of time-periodic solutions and spatially localised solutions (breathers), in general nonlinear Klein-Gordon infinite lattices. The existence problem is converted into a fixed point problem for an operator on some…
In this work, we consider germs of analytic singular vector elds in (C^3,0) with an isolated and doubly-resonant singularity of saddle-node type at the origin. Such vector elds come from irregular two-dimensional dierential systems with two…
The real Ginzburg-Landau equation possesses a family of spatially periodic equilibria. If the wave number of an equilibrium is strictly below the so called Eckhaus boundary the equilibrium is known to be spectrally and diffusively stable,…
We study, analytically and numerically, the dynamical behavior of the solutions of the complex Ginzburg-Landau equation with diffraction but without diffusion, which governs the spatial evolution of the field in an active nonlinear laser…
We consider a notion of stability for sheaves, which we call multi-Gieseker stability that depends on several ample polarisations $L_1, \dots, L_N$ and on an additional parameter $\sigma \in \mathbb{Q}_{\geq 0}^N\setminus\{0\}$. The set of…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
We give a generalization, in the context of sheaves, of a classical result of Grothendieck concerning the integrability of connections of type $(0,1)$ over a ${\cal C}^{\infty}$ vector bundle over a complex manifold. We introduce the notion…
We study a complex Ginzburg-Landau (GL) type model related to fluid instabilities in the boundary of magnetized toroidal plasmas (called edge-localized modes) with a prescribed shear flow on the Neumann boundary condition. We obtain the…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
We provide a rigorous analysis for the so-called endlessly continuable germs of holomorphic functions or in other words, the Ecalle's resurgent functions. We follow and complete an approach due to Pham, based on the notion of discrete…
The formal class of a germ of diffeomorphism $\phi$ is embeddable in a flow if $\phi$ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at…