相关论文: Stationary solutions to coagulation-fragmentation …
We consider a Liouville-type PDE on a smooth bounded planar domain, which is related to stationary solutions of the Keller-Segel's model for chemotaxis. We prove existence of solutions under some algebraic conditions on the parameters. In…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
In this paper, we show the existence and uniqueness of the stationary solution $u(t,\omega)$ and stationary point $Y(\omega)$ of the differentiable random dynamical system $U:R\times L^2[0,1]\times \Omega\to L^2[0,1]$ generated by the…
To the Yang-Baxter equation an additional relation can be added. This is the reflection equation which appears in various places, with or without spectral parameter. For example, in factorizable scattering on a half-line, integrable lattice…
We consider Smoluchowski's equation with a homogeneous kernel of the form $a(x,y) = x^\alpha y ^\beta + x^\beta y^\alpha$ with $-1 < \alpha \leq \beta < 1$ and $\lambda := \alpha + \beta \in (-1,1)$. We first show that self-similar…
In this work, the power series solutions are given around a regular-singular point, in the case of variable coefficients for homogeneous sequential linear conformable fractional differential equations of order 2{\alpha}.
In this paper we establish the uniqueness of a solution to a stationary convection-diffusion equation in divergence form with an exponentially summable generalized divergence-free drift.
We study stationary solutions to the Keller--Segel equation on curved planes. We prove the necessity of the mass being $8 \pi$ and a sharp decay bound. Notably, our results do not require the solutions to have a finite second moment, and…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
Asymptotic expressions for an integral appearing in the solution of a d-bar problem are presented. The integral is a solid Cauchy transform of a function with a rapidly oscillating phase with a small parameter $h$, $0<h\ll 1$. Whereas…
Existence and uniqueness of mass-conserving classical solutions to the continuous coagulation equation with collisional breakage are investigated for an unbounded class of collision kernels and a particular case of the distribution…
In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with $m\geq 2$ population densities. We introduce a discrete multi-phase…
In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…
We consider a functional semilinear Rayleigh-Stokes equation involving fractional derivative. Our aim is to analyze some circumstances, in those the global solvability and some results on asymptotic behavior of solutions take place. By…
In this article, the existence of mass-conserving solutions is investigated to the continuous coagulation and collisional breakage equation with singular coagulation kernels. Here, the probability distribution function attains singularity…
This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: \[ \left(\partial^\beta+\frac{\nu}{2}(-\Delta)^{\alpha/2}\right)u(t,x) =…
Existence and uniqueness of weak solutions to the collision-induced breakage and coag-ulation equation are shown when coagulation is the dominant mechanism for small volumes. The collision kernel may feature a stronger singularity for small…
We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space $\mathbb{R}^d$, $d \ge 3$, under the assumption that weak solutions of the…
The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. This is done including both Poynting-Robertson effect and stellar wind. The solutions are stationary in semimajor…