Related papers: Growth Equation with Conservation Law
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…
It is shown that the `conservation law' for metric fluctuations with long wavelengths is indeed applicable for growing modes of perturbations, which are of interest in cosmology, in spite of a recent criticism [L. P. Grishchuk, Preprint…
A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analyzed and…
A method based on the kinetics of adatoms on a growing surface under epitaxial growth at low temperature in (1+1) dimensions is proposed to obtain a closed form of local growth equation. It can be generalized to any growth problem as long…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
We prove quantitative growth estimates for large data solutions to the 1D Boltzmann equation, for a collision kernel with angular cutoff and relative velocity cutoff. We present proofs for the global well-posedness results presented in the…
We consider generalizations of the Kardar--Parisi--Zhang equation that accomodate spatial anisotropies and the coupled evolution of several fields, and focus on their symmetries and non-perturbative properties. In particular, we derive…
In this paper, we present infinitely many conserved densities satisfying particular conservation law $F_{t}=(2uF)_{x}$ for the generalized Riemann equations at $N=2,3,4$. In the $N=2$ case, we also construct conserved densities…
Using the dynamic renormalization group (DRG) technique, we analyze general nonlinearities in a conservative nonlinear growth equation with non-conserved gaussian white noise. We show that they fall in two classes only: the…
The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including…
The self-alignment concentrations, $c(x)$, as functions of the length, $x$, of the identically matching maximal segments in the genomes of a variety of species, typically present power-law tails extending to the largest scales, i.e., $c(x)…
In a wide range of physical phenomena, we find propagating surfaces {\Omega}t which need mathematical treatment. In this article, we review the theory of the system of kinematical conservation laws (KCL), which govern the evolution of these…
We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a {\it general bulk growth model} by means of a continuum Master equation for the evolution of the bulk…
We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential-type approximation of the Dirac distribution. This enables…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et…
In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle.…
Monod's law is a widely accepted phenomenology for bacterial growth. Since it has the same functional form as the Michaelis--Menten equation for enzyme kinetics, cell growth is often considered to be locally constrained by a single…
In this paper, we address the question of estimating the energy decay of integro-differential evolution equations with glassy memory. This class of memory kernel was not analyzed in previous studies. Moreover, a detailed analysis provides…