Results 91 to 100 of about 1,301 (120)

Reaction-diffusion systems with 1-homogeneous non-linearity

Electronic Journal of Differential Equations, 2002
We describe the dynamics of a system of two reaction-diffusion equations with 1-homogeneous non-linearity. We show that either an order-preserving property holds and can be used in order to determine the limiting behaviour in some (invariant) sets or the
Matthias Bueger
doaj  

The Quenching Problem in the Nonlinear Heat Equations [PDF]

arXiv, 2006
In this paper we study the quenching problem in nonlinear heat equations with power nonlinearities. For nonlinearities of power p<0 and for an open set of slowly varying initial conditions we prove that the solutions will collapse in a finite time. We find the collapse profile and estimate the remainder.
arxiv  

Attractors for reaction-diffusion equations on arbitrary unbounded domains [PDF]

arXiv, 2007
We prove existence of global attractors for parabolic equations of the form $$u_t+\beta(x)u-\sum_{ij}\partial_i(a_{ij}(x)\partial_j u)=f(x,u)$$ with Dirichlet boundary condition on an arbitrary unbounded domain $\Omega$ in $\R^3$, without smoothness assumptions on $a_{ij}(\cdot)$ and $\partial\Omega$.
arxiv  

IMEX method convergence for a parabolic equation [PDF]

arXiv, 2007
Although implicit-explicit (IMEX) methods for approximating solutions to semilinear parabolic equations are relatively standard, most recent works examine the case of a fully discretized model. We show that by discretizing time only, one can obtain an elementary convergence result for an implicit-explicit method.
arxiv  

Generalized result on the global existence of positive solutions for a parabolic reaction-diffusion model with an m × m diffusion matrix

Demonstratio Mathematica
The aim of this work is to study the global existence in time of solutions for the tridiagonal system of reaction-diffusion by order mm. Our techniques of proof are based on compact semigroup methods and some L1{L}^{1}-estimates.
Barrouk Nabila, Abdelmalek Karima
doaj   +1 more source

Computation of solution to fractional order partial reaction diffusion equations

Journal of Advanced Research, 2020
In this article, the considered problem of Cauchy reaction diffusion equation of fractional order is solved by using integral transform of Laplace coupled with decomposition technique due to Adomian scheme.
Haji Gul, Hussam Alrabaiah, Sajjad Ali, Kamal Shah, Shakoor Muhammad   +4 more
doaj  

Dynamics of particulate emissions in the presence of autonomous vehicles

Open Mathematics
Around one third of CO2{{\rm{CO}}}_{2} emissions in the atmosphere are linked to vehicular traffic. Pollutant agents have an impact on the environment, in particular, the increased presence of particulate matter (PM) creates negative effects on human ...
Briani Maya, Denaro Christopher Anthony, Piccoli Benedetto, Rarità Luigi   +3 more
doaj   +1 more source

Sharp Asymptotics for KPP Pulsating Front Speed-up and Diffusion Enhancement by Flows [PDF]

arXiv, 2007
We study KPP pulsating front speed-up and effective diffusivity enhancement by general periodic incompressible flows. We prove the existence of and determine the limits $c^*(A)/A$ and $D(A)/A^2$ as $A\to\infty$, where $c^*(A)$ is the minimal front speed and $D(A)$ the effective diffusivity.
arxiv  

Stability and instability of constant stationary solutions to some integro-differential equations [PDF]

arXiv
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 nontrivial constant stationary solutions.
arxiv  

Persistence of pulses for certain reaction-diffusion equations in dimensions two and three [PDF]

arXiv
We address the persistence under a perturbation of stationary pulse solutions of some reaction-diffusion type equations in dimensions d=2,3 and evaluate the asymptotic approximations of such pulses to the leading order in the parameter of the perturbation.
arxiv