Related papers: Cauchy problem for multiscale conservation laws: A…
We introduce the notion of entropy solutions (e.s.) to a conservation law with an arbitrary jump continuous flux vector and prove existence of the largest and the smallest e.s. to the Cauchy problem. The monotonicity and stability…
We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a~kinetic formulation…
We {\it analytically} investigate the population and coherence dynamics and relaxations in the vibrational energy transport in molecules. The corresponding two time scales $t_1$ and $t_2$ are explored. Coherence-population entanglement is…
The prevalence of sexual reproduction ("sex") in eukaryotes is an enigma of evolutionary biology. Sex increases genetic variation only tells its long-term superiority in essence. The accumulation of harmful mutations causes an immediate and…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
Evolutionary game dynamics are often studied in the context of different population structures. Here we propose a new population structure that is inspired by simple multicellular life forms. In our model, cells reproduce but can stay…
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
The data we analyze derives from the observation of numerous cells of the bacterium Escherichia coli (E. coli) growing and dividing. Single cells grow and divide to give birth to two daughter cells, that in turn grow and divide. Thus, a…
In this paper we consider a class of $p$-evolution equations of arbitrary order with variable coefficients depending on time and space variables $(t,x)$. We prove necessary conditions on the decay rates of the coefficients for the…
In species reproducing both sexually and asexually clones are often more common in recently established populations. Earlier studies have suggested that this pattern arises from natural selection favouring asexual recruitment in young…
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…
Boundary-catalytic branching processes describe a broad class of natural phenomena where the population of diffusing particles grows due to their spontaneous binary branching (e.g., division, fission or splitting) on a catalytic boundary…
The evolution of structure in biology is driven by accretion and change. Accretion brings together disparate parts to form bigger wholes. Change provides opportunities for growth and innovation. Here we review patterns and processes that…
As a tool for understanding the meridional circulation of the atmosphere, a two-dimensional ( latitude -- height ) numerical model is used to clarify the relationship between the Hadley circulation and large-scale motions associated with…
We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type…
We consider generalized models on coral broadcast spawning phenomena involving diffusion, advection, chemotaxis, and reactions when egg and sperm densities are different. We prove the global-in-time existence of the regular solutions of the…
We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, where the exponent satisfies the doubling condition. In particular, both the so called logconvex and…