Related papers: Diffusion-convection reaction equations with sign-…
Reaction-diffusion equations are widely used to describe a variety of phenomena such as pattern formation and front propagation in biological, chemical and physical systems. In the one-dimensional model with a balanced bistable reaction…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature)…
We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion-reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of…
Under low-Reynolds-number conditions, dynamics of convection and diffusion are usually considered separately because their dominant spatial and temporal scales are different, but cooperative effects of convection and diffusion can cause…
The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are…
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique…
In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of one-dimensional reaction-diffusion equations. Such reaction-diffusion equations include the classical model of…
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
In this report we investigate the regularity of the solution to the fractional diffusion, advection, reaction equation on a bounded domain in $\mathbb{R}^{1}$. The analysis is performed in the weighted Sobolev spaces, $H_{(a ,…
We study existence and uniqueness of travelling fronts, and asymptotic speed of propagation for a non local reaction diffusion equation with spatial and genetic trait structure.
Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic…
Convection is ubiquitous in stellar and planetary interiors where it likely plays an integral role in the generation of magnetic fields. As the interiors of these objects remain hidden from direct observation, numerical models of convection…