Results 21 to 30 of about 148 (125)

On the Resolution of Some Itô Diffusions by the Heat Equation

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
We consider a class of partial differential equations that arise from one‐dimensional generalized square root problems, featuring drift and diffusion. In particular, we investigate models whereby a diffusion coefficient is described by a power law.
Sameerah Jamal, Elena Kaikina
wiley   +1 more source

The Impact of Imperfect Vaccination on Infectious Disease Transmission in an Age-Structured Population [PDF]

In this paper, we consider the influence of imperfect vaccination on the spread of infectious diseases in an age-structured population. The benefits of vaccination, even if not perfect, generally outweigh the risks of severe diseases.
Touaoula, Tarik Mohammed, Hathout, Fatima Zohra   +1 more
core   +1 more source

Boundedness and stabilization in a three-species chemotaxis-competition system with singular sensitivity

Advances in Nonlinear Analysis
This paper deals with the following fully parabolic chemotaxis system with singular sensitivity and Lotka–Volterra competition kineticsut=Δu−χ1∇⋅uz∇z+μ1u(1−u−a12v−a13ω),x∈Ω,t>0,vt=Δv−χ2∇⋅vz∇z+μ2v(1−a21u−v−a23ω),x∈Ω,t>0,ωt=Δω−χ3∇⋅ωz∇z+μ3ω(1−a31u−a32v−ω),x∈
Zhu Zhangsheng
doaj   +1 more source

Quantitative Nonlocal‐to‐Local Limits in Multispecies Interaction Systems via Relative Entropy and Modulated Energy

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
We derive quantitative convergence rates for nonlocal‐to‐local limits in a class of multispecies interaction systems with finite‐range kernels. The nonlocal model consists of coupled aggregation–diffusion equations in which intra‐ and interspecies interactions are mediated by short‐range convolution operators.
S. C. Oukouomi Noutchie, John Venetis
wiley   +1 more source

Linear asymptotic stability of a free boundary problem modeling tumor growth with two-phase Stokes equations

Advances in Nonlinear Analysis
In this paper, we consider a two-phase fluid tumor model by assuming that the tumor and its growth environment are two incompressible fluids with different viscosities.
Wu Junde, Ren Yanting
doaj   +1 more source

Fundamental Transformations to Inhomogeneous Parabolic PDEs

Journal of Mathematics, Volume 2025, Issue 1, 2025.
The present paper is devoted to inhomogeneous (1 + 1) parabolic equations. In particular, we find a mapping which transforms the equations into a target equation. We prove a necessary condition which allows for the inhomogeneity to vanish. Consequently, we provide a concise presentation on a method of integrability of these equations.
Sameerah Jamal, Guotao Wang
wiley   +1 more source

A degenerate migration-consumption model in domains of arbitrary dimension

Advanced Nonlinear Studies
In a smoothly bounded convex domain Ω⊂Rn ${\Omega}\subset {\mathbb{R}}^{n}$ with n ≥ 1, a no-flux initial-boundary value problem forut=Δuϕ(v),vt=Δv−uv, $$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv ...
Winkler Michael
doaj   +1 more source

Modelling the cell cycle [PDF]

, 2015
This thesis may be divided into two related parts. The rst of which considers a population balance approach to modelling a population of cells, with particular emphasis on how the cells pass between the G1 and S phases of the cell cycle.
Chaffey, Gary S.
core  

Boundedness and long-time behavior in a parabolic-elliptic system arising from biological transport networks

Advances in Nonlinear Analysis
The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the ...
Li Bin
doaj   +1 more source

Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “
Ion Stelian, Cruceanu Stefan-Gicu, Marinescu Dorin   +2 more
doaj   +1 more source