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We derive guaranteed bounds of distance to the exact solution of the evolutionary reaction-diffusion problem with mixed Dirichlet-Neumann boundary condition. It is shown that two-sided error estimates are directly computable and equivalent…
This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…
Evolutionary computation offers a variety of tools to solve complex real-world optimization problems. However, research often focuses on smaller, simplified problems and optimization algorithms that sometimes miss expectations in real-world…
Evolutionary game theory combines game theory and dynamical systems and is customarily adopted to describe evolutionary dynamics in multi-agent systems. In particular, it has been proven to be a successful tool to describe multi-agent…
The behavior near the extinction time is identified for non-negative solutions to the diffusive Hamilton-Jacobi equation with critical gradient absorption $\partial_t u - \Delta_p u + |\nabla u|^{p-1} = 0$ in $(0, \infty) \times…
We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all…
Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for…
We find a continuum of extinction rates for solutions $u(y,\tau)\ge 0$ of the fast diffusion equation $u_\tau=\Delta u^m$ in a subrange of exponents $m\in (0,1)$. The equation is posed in $\ren$ for times up to the extinction time $T>0$.…
We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual…
In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexual adaptation such as the…
We study the long time behavior of a parabolic Lotka-Volterra type equation considering a time-periodic growth rate with non-local competition. Such equation describes the dynamics of a phenotypically struc-tured population under the effect…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…
We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations based on the time-independent Schr\"{o}dinger equation for a quantum particle subjected to a uniform…
We study the evolutionary dynamics of an asexual population of nonmutators and mutators on a class of epistatic fitness landscapes. We consider the situation in which all mutations are deleterious and mutators are produced from nonmutators…
We analyze a reaction-diffusion system on $\mathbb{R}^{N}$ which models the dispersal of individuals between two exchanging environments for its diffusive component and incorporates a Fujita-type growth for its reactive component. The…
The aim of this paper is to refine some results concerning the blow-up of solutions of the exponential reaction-diffusion equation. We consider solutions that blow-up in finite time, but continue to exist as weak solutions beyond the…
Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a driving force $f(u)$ that depends on the state variable $u$…
We consider an abstract second order evolution equation with damping. The "elastic" term is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the origin. We…
We consider a cyclically competing species model on a ring with global mixing at finite rate, which corresponds to the well-known Lotka-Volterra equation in the limit of infinite mixing rate. Within a perturbation analysis of the model from…