Related papers: Existence, uniqueness and decay rates for evolutio…
We are interested in the relative conditioning of the problem $y_0\mapsto \mathrm{e}^{tA}y_0$, i.e., the relative conditioning of the action of the matrix exponential $\mathrm{e}% ^{tA}$ on a vector with respect to perturbations of this…
In this note, we study the asymptotic behavior, as $t$ tends to infinity, of the solution $u$ to the evolutionary damped $p$-Laplace equation \begin{equation*} u_{tt}+a\, u_t =\Delta_p u \end{equation*} with Dirichlet boundary values. Let…
In this article we consider a class of state-dependent delay differential equations which is modelling the dynamics of the number of adult trees in forests. We prove the boundedness of solutions for a single species model as well as a…
Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a…
We consider conditions for the decay in time of solutions of non-homogenous hyperbolic equations. It is proven that solutions of the equations go to $0$ in $L^2$ at infinity if and only if an equation's right-hand side uniquely determines…
Using German forest health monitoring data we investigate the main drivers leading to tree mortality and the association between defoliation and mortality; in particular (a) whether defoliation is a proxy for other covariates (climate,…
If evolution can be connected to the principle of least action, and if it is depicted in evolution space versus time then it corresponds to the direction of ultimate causation. As an organism evolves and follows a path of proximate…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We address the study of decay rates of solutions to dissipative equations. The characterization of these rates is given for a wide class of linear systems by the {\em decay character}, which is a number associated to the initial datum that…
In this paper, we study the Cauchy problem to the linear damped $\sigma$-evolution equation with time-dependent damping in the effective cases \begin{equation*} u_{t t}+(-\Delta)^\sigma u+b(t)(-\Delta)^\delta u_t=0, \end{equation*} and…
Exact law of mortality dynamics in changing populations and environment is derived. The law is universal for all species, from single cell yeast to humans. It includes no characteristics of animal- environment interactions (metabolism etc)…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
Let a fourth and a second order evolution equations be coupled via the interface by transmission conditions, and suppose that the first one is stabilized by a localized distributed feedback. What will then be the effect of such a partial…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…
In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are…