Related papers: Nonlinearities in Conservative Growth Equations
We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in $D$ dimensions coupled to a $q$-form field and positive cosmological constant. We show that…
We study a class of one-dimensional, nonequilibrium, conserved growth equations for both nonconserved and conserved noise statistics using numerical integration. An atomistic version of these growth equations is also studied using…
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the limiting behavior of solutions to SdNLW with regularized…
We study the general (2+1)-dimensional Davey-Stewartson (DS) equations with nonlinear and gain terms and acquire explicit solutions through variable separation approach. In particular, we deduce some main novel excitations for the DS…
We survey recent advances in the analysis of the large data global (and asymptotic) behaviour of nonlinear dispersive equations such as the nonlinear wave (NLW), nonlinear Schr\"odinger (NLS), wave maps (WM), Schr\"odinger maps (SM),…
Aim of the paper is the qualitative analysis of a quasi-linear parabolic third order equation, which describes the evolution in a large class of dissipative models. As examples of some typical boundary problems, both Dirichlet's and…
We discuss a variational approach to doubly nonlinear wave equations of the form $\rho u_{tt} + g (u_t) - \Delta u + f (u)=0$. This approach hinges on the minimization of a parameter-dependent family of uniformly convex functionals over…
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…
Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for…
In this paper, we study the equilibrium states of a $N\times N$ stochastic complex random matrix $M$, whose entries evolve in time accordingly with a Langevin equation including both Gaussian white noises and a linear disorder, materialized…
In the present study we are interested in the Davey-Stewartson equations (DSE) that model packets of surface and capillary-gravity waves. We focus on the elliptic-elliptic case, for which it is known that DSE may develop a finite-time…
From the work on the weak-null condition by Lindblad and Rodnianski, it is well-known that `bad' quadratic sourcing terms are allowed to appear in coupled semilinear wave equations in three spatial dimensions, provided that such terms…
It has been known for some time that 2-loop renormalization group (RG) equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed…
We study the growth of large scale structure in two recently proposed non-standard cosmological models: the brane induced gravity model of Dvali, Gabadadze and Porrati (DGP) and the Cardassian models of Freese and Lewis. A general formalism…
We consider partial differential equations (PDE) of drift-diffusion type in the unit interval, supplemented by either two conservation laws or by a conservation law and a further boundary condition. We treat two different cases: (i) uniform…
We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such operators is the degenerate anisotropic…
Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic…
The standard analytic solution of the renormalization group (RG) evolution for the $\Delta S = 1$ Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution…
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…
We develop a new approach to study the nonlinear evolution in the large-scale structure of the Universe both in real space and in redshift space, extending the standard perturbation theory of gravitational instability. Infinite series of…