Related papers: Diffusion-convection reaction equations with sign-…
Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered…
This paper is devoted to a nonlocal reaction-diffusion-advection model that describes the spatial dynamics of freshwater organisms in a river with a directional motion. Our goal is to investigate how the advection rate affects the dynamic…
A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations…
We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the $L^q$-energy inequality and speed estimate in Wasserstein spaces under some integrability conditions on the drift term.…
We study front propagation in the reversible reaction-diffusion system A + A <-> A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame…
Due to its parabolic character, the diffusion equation exhibits instantaneous spatial spreading, and becomes unstable when Lorentz-boosted. According to the conventional interpretation, these features reflect a fundamental incompatibility…
We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested…
The aim of this paper is to study the existence and the geometry of positive bounded wave solutions to a non-local delayed reaction-diffusion equation of the monostable type.
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator plus an indefinite potential. In the reaction we have the competing effects of a singular term and of concave and convex nonlinearities. In this…
We present an analysis of existence, uniqueness, and smoothness of the solution to a class of fractional ordinary differential equations posed on the whole real line that models a steady state behavior of a certain anomalous diffusion,…
In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive that the solution is positive when the source term is nonpositive by a subordination principle for the solution. As an…
We prove the existence of a continuous family of positive and generally non-monotone travelling fronts in delayed reaction-diffusion equations $u_t(t,x) = \Delta u(t,x)- u(t,x) + g(u(t-h,x)) (*)$, when $g \in C^2(R_+,R_+)$ has exactly two…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using…