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This document comes as supplementary material of the paper Stability in Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a number of classical or elementary statements concerning constants and inequalities for…
We study the stability of the bubble rising in the presence of a soluble surfactant numerically and experimentally. For the surfactant concentration considered, the Marangoni stress almost immobilizes the interface. However, the non-zero…
Given two planar, conformal, smooth open sets $\Omega$ and $\omega$, we prove the existence of a sequence of smooth sets $\Omega_n$ which geometrically converges to $\Omega$ and such that the (perimeter normalized) Steklov eigenvalues of…
This paper has been withdrawn by the author due to a gap in the proof of the main result.
Novel criteria for global asymptotic stability of nonlinear uncertain finite-dimensional systems are presented. The results are obtained by a combination of the "discretization approach" and the ideas contained in the proof of the original…
We present a brief overview of the stability analysis of the Einstein static universe in various modified theories of gravity, like f(R) gravity, Gauss-Bonnet or f(G) gravity, and Horava-Lifshitz gravity.
We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.
In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition which allows us to prove the global nonlinear asymptotic stability…
We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the…
The paper has been withdrawn by authors. The issues studied in this paper were changed so much that we have published a new paper considering these issues. See hep-th/0406074
We show a strong Hamiltonian stability result for a simpler and larger distance on the Tamarkin category. We also give a stability result with support conditions.
In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*}…
We prove global in time dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. We assume neither the smallness of the relative slope of the nozzle nor the weakness of the shock. Key ingredients…
This paper investigates the existence and stability of Einstein universe in the context of $f(R,T,Q)$ gravity, where $Q=R_{\mu\nu}T^{\mu\nu}$. Considering linear homogeneous perturbations around scale factor and energy density, we formulate…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.
In two and three space dimensions, and under suitable assumptions on the initial data, we show global existence for a damped wave equation which approaches, in some sense, the Navier-Stokes problem. The proofs are based on a refined energy…
This paper was withdrawn by the author due to an error in the proof of the main result; essentially the parameter R used in the proof may depend on the manifold (M, g), not just on dimension and pinching constant.
Building upon the technique that we developed earlier for perturbed sweeping processes with convex moving constraints and monotone vector fields (Kamenskii et al, Nonlinear Anal. Hybrid Syst. 30, 2018), the present paper establishes global…
The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid…