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In this note, we show that there exist solutions of the Muskat problem which shift stability regimes in the following sense: they start stable, then become unstable, and finally return back to the stable regime. This proves existence of…
In this paper, we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions. Non-existence result is…
This paper has been withdrawn by the author due to a serious flaw that needs to be fixed. That is in progress by the author.
We derive analogues of the classical Rayleigh, Fjortoft and Arnold stability and instability theorems in the context of the 2D $\alpha$-Euler equations.
This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.
The paper is being withdrawn since the results are incorporated in paper arxiv.org/abs/math.AG/0306195.
We analyze the stability of the Einstein static universe by considering homogeneous perturbations in the context of f(G) modified Gauss-Bonnet theories of gravity. By considering a generic form of f(G), the stability region of the Einstein…
Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Ho\v{r}ava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition…
The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy…
This paper is devoted to the analysis of global stability of the chemostat system with a perturbation term representing any type of exchange between species. This conversion term depends on species and substrate concentrations but also on a…
In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on…
This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.
We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and…
Proceeded from the gravitation equations proposed by one of authors it was argued in a previous paper that there can exist supermassive compact configurations of degenerated Fermi-gas without events horizon. In the present paper we consider…
This paper is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz-Slyozov-Wagner (LSW) system in the case when the initial data has compact support. The…
Based on the domain variational point of view, we carry on stability analysis on two shape optimization problems from thermal insulation background. The novelty is that, we do not require that the second variation is normal to the boundary.…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the…
We comment on the stability analysis of alpha-quartz under pressure by Gregoryanz et al., Phys. Rev. Lett. 84, 3117 (2000). The proper stability criterion for solids under pressure has to be formulated in terms of Birch coefficients rather…
The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.