Related papers: Existence theory for a bushfire equation
Tree-grass coexistence in savanna ecosystems depends strongly on environmental disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect…
We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…
The problem of the diffusion evolution of a pore filled with molecular hydrogen in a spherical granule in a hydrogen medium is solved. The initial position of the pore is displaced relative to the center of the granule. A nonlinear system…
In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…
We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to recent trends in diffusion theory: considering anomalous…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…
We study a nonlinear evolutionary partial differential equation that can be viewed as a generalization of the heat equation where the temperature gradient is a~priori bounded but the heat flux provides merely \mbox{$L^1$-coercivity}.…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of…
The goal of this work is to establish the global existence of nonnegative classical solutions in all dimensions for a system of highly nonlinear reaction-diffusion equations. We address the case for different diffusion coefficients and the…
The dynamics of flame propagation in systems with infinite Lewis number and spatially discretized sources of heat release is examined, which is applicable to the combustion of suspensions of fuel particles in air. The system is analyzed…
We consider a nonlocal semi-linear parabolic equation on a connected exterior domain of the form $\mathbb{R}^N\setminus K$, where $K\subset\mathbb{R}^N$ is a compact "obstacle". The model we study is motivated by applications in biology and…
This paper is concerned with the existence and uniqueness of transition fronts of a general reaction-diffusion-advection equation in domains with multiple branches. In this paper, every branch in the domain is not necessary to be straight…
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…
It is well-known that quadratic or cubic nonlinearities in reaction-diffusion-advection systems can lead to growth of solutions with small, localized initial data and even finite time blow-up. It was recently proved, however, that, if the…
We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
In this paper, diffusion in polymer solutions undergoing evaporation of solvent is modeled as a coupled heat and mass transfer problem with moving boundary condition within the framework of nonequilibrium thermodynamics. The proposed…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…