Related papers: Evolutionary Game Theory on Measure Spaces: Well-P…

In the article we establish the global well-posedness in W^{1, 2, 2}(R\times R^{+}) of the integro-differential equation in the case of the anomalous diffusion when the one dimensional negative Laplace operator is raised to a fractional…

This tutorial article puts forth a framework to analyze the noncooperative strategic interactions among the members of a large population of bounded rationality agents. Our approach hinges on, unifies and generalizes existing methods and…

We prove short-time well-posedness and existence of global weak solutions of the Beris--Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system…

We consider different concepts of well-posedness and ill-posedness and their relations for solving nonlinear and linear operator equations in Hilbert spaces. First, the concepts of Hadamard and Nashed are recalled which are appropriate for…

The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century there have been remarkable advances in the development of theory for this diversification, and the theory's success…

We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution…

The work is devoted to the global well-posedness in W^{1, (4, 2)}(R\times R^{+}) of the integro-differential problem involving the square of the one dimensional Laplace operator along with the drift term. Our proof is based on a fixed point…

We establish the first unconditional well-posedness result for the master equation associated with a general class of mean field games of controls. Our analysis covers games with displacement monotone or Lasry--Lions monotone data, as well…

We adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions $u$ and $v$. We consider a…

We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential $K$. We are interested in establishing their well-posedness theory when the nonlocal interaction potential $K$ is neither differentiable nor…

We study the long-time behavior of solutions to a measure-valued selection-mutation model that we formulated in \cite{CLEVACK}. We establish permanence results for the full model, and we study the limiting behavior even when there is more…

We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…

In population games, a large population of players, modeled as a continuum, is divided into subpopulations, and the fitness or payoff of each subpopulation depends on the overall population composition. Evolutionary dynamics describe how…

We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…

The elapsed time equation is an age-structured model that describes the dynamics of interconnected spiking neurons through the elapsed time since the last discharge, leading to many interesting questions on the evolution of the system from…

In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (arXiv:1804.11290) by the same authors, general well-posedness results have been established for a a class of evolutionary systems of two…

We characterize the well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation. This class includes in particular the Euler-Bernoulli beam equations and more generally 1D linear…

In this work, a theorem is first proved which presents a game theoretic formulation of a necessary and sufficient sustainizability over a set condition for a general system described by ordinary differential equations (ODEs). Then, two…

In games with continuous strategy spaces, if a rest point of the replicator dynamics is asymptotically stable then the rest point must be finitely supported (van Veelen, M., Spreij, P., 2009. Evolution in games with a continuous action…

In this paper, we extend a class of globally convergent evolution strategies to handle general constrained optimization problems. The proposed framework handles relaxable constraints using a merit function approach combined with a specific…