Related papers: Stability of solutions to stochastic partial diffe…
This paper studies stabilities of stochastic differential equation (SDE) driven by time-changed L\'evy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics,…
In this paper we focus on the pathwise stability of mild solutions for a class of stochastic partial differential equations which are driven by switching-diffusion processes with jumps. In comparison to the existing literature, we show…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDE of KdV-type, including generalized KdV and Benjamin-Ono equations. In this investigation, we consider the…
We propose a quantitative direct method of proving the stability result for Gaussian rough differential equations in the sense of Gubinelli \cite{gubinelli}. Under the strongly dissipative assumption of the drift coefficient function, we…
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…
We study strong existence and pathwise uniqueness for stochastic differential equations in $\RR^d$ with rough coefficients, and without assuming uniform ellipticity for the diffusion matrix. Our approach relies on direct quantitative…
We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
We consider Mc Kean-Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. This type of SDEs…
In this thesis, we explore several related topics broadly regarding the symmetry and geometric properties of nonlocal partial differential equations (PDE). This thesis is split into three parts. In the first part, we study two…
We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous…