Related papers: Exponentially long time stability for non--lineari…
We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local…
The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to…
In this paper, we establish Gevrey class regularity of solutions to a class of dissipative equations with an analytic nonlinearity in the whole space. This generalizes the results of Ferrari and Titi in the periodic space case with initial…
We perform the nonlinear stability analysis of a chemotaxis model of bacterial self-organization, assuming that bacteria respond sharply to chemical signals. The resulting discontinuous advection speed represents the key challenge for the…
The rational homology groups of the packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre--Veronese varieties). These complexes…
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an…
We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is…
The center $\mathscr{Z}_n(q)$ of the integral group algebra of the general linear group $GL_n(q)$ over a finite field admits a filtration with respect to the reflection length. We show that the structure constants of the associated graded…
We establish long-time stability of multi-dimensional noncharacteristic boundary layers of a class of hyperbolic--parabolic systems including the compressible Navier--Stokes equations with inflow [outflow] boundary conditions, under the…
We study the asymptotic stability of traveling fronts and front's velocity selection problem for the time-delayed monostable equation $(*)$ $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),\ x \in \mathbb{R},\ t >0$, considered with…
In the paper, we study the Prandtl system with initial data admitting non-degenerate critical points. For any index $\sigma\in[3/2, 2],$ we obtain the local in time well-posedness in the space of Gevrey class $G^\sigma$ in the tangential…
We present conditions on families of diffeomorphisms that guarantee statistical stability and SRB entropy continuity. They rely on the existence of horseshoe-like sets with infinitely many branches and variable return times. As an…
We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in…
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
Let $f(z) = e^{2\pi i \alpha}z + O(z^2), \alpha \in \mathbb{R}$ be a germ of holomorphic diffeomorphism in $\mathbb{C}$. For $\alpha$ rational and $f$ of infinite order, the space of conformal conjugacy classes of germs topologically…
We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…
We study critical points of the Ginzburg-Landau (GL) functional and the abelian Yang-Mills-Higgs (YMH) functional on the sphere and the complex projective space, both equipped with the standard metrics. For the GL functional we prove that…
Let $f$ be a germ of holomorphic diffeomorphism with an irrationally indifferent fixed point at the origin in $\mathbb{C}$ (i.e. $f(0) = 0, f'(0) = e^{2\pi i \alpha}, \alpha \in \mathbb{R} - \mathbb{Q}$). Perez-Marco showed the existence of…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…