Spatiotemporal chaos (STC) exhibited by the Kuramoto-Sivashinsky (KS) equation is investigated analytically and numerically. An eeective stochastic equation belonging to the KPZ universality class is constructed by incorporating the chaotic dynamics of the small KS system in a coarse-graining procedure. The bare parameters of the eeective theory are computed approximately. Stability of the syst...

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretical extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally reduced description for such systems. The neglected degrees of freedom by this reduction are replaced by a systematically defined stochastic process under a co...

The spatial scaling law and intermittency of the V2O5 surface roughness has been investigated by atomic force microscopy. The intermittency of the height fluctuations has been checked by two different methods, first, by measuring the scaling exponent of the qth moment of height-difference fluctuations i.e. Cq = 〈|h(x1)− h(x2)|q〉, and second, by defining the generating function Z(q, N) and gener...

We study the emergence of pattern formation and chaotic dynamics in the one-dimensional (1D) generalized Kuramoto-Sivashinsky (gKS) equation by means of a time-series analysis, in particular a nonlinear forecasting method which is based on concepts from chaos theory and appropriate statistical methods. We analyze two types of temporal signals, a local one and a global one, finding in both cases...

In suitable parameter regimes the Integral Boundary Layer equation (IBLe) can be formally derived as a long wave approximation for the flow of a viscous incompressible fluid down an inclined plane. For very long waves with small amplitude, the IBLe can be further reduced to the Kuramoto–Sivashinsky equation (KSe). Here we justify this reduction of the IBL to the KSe. Using energy estimates we s...

In this article, we present an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability for this inverse problem is our main result a...

We consider the Kuramoto-Sivashinsky (KS) equation in finite domains of the form [−L, L]. Our main result provides effective new estimates for higher Sobolev norms of the solutions in terms of powers of L for the onedimentional differentiated KS. We illustrate our method on a simpler model, namely the regularized Burger’s equation. The underlying idea in this result is that a priori control of ...

A shock-like structure appears in a time-averaged pattern produced by the Kuramoto-Sivashinsky equation and the noisy Burgers equation with fixed boundary conditions. We show that the effective viscosity computed from the width of the time-averaged shock structure is consistent with that computed from the time correlation of the fluctuations. The effective viscosity depends on the lengthscale, ...

In this article, we consider a non-local variant of the Kuramoto-Sivashinsky equation in three dimensions (2D interface). Besides showing global wellposedness also obtain some qualitative properties solutions. particular, prove that solutions become analytic spatial variable for positive time, existence compact attractor and an upper bound on number oscillations We observe such is particularly ...

The Kuramoto-Sivashinsky equation is a fourth-order partial differential used as model for physical phenomena such plane flame propagation and phase of turbulence. inverse problem recovering the second-order coefficient from knowledge solution in final time, linear version equation, studied this article. formulated regularized nonlinear optimization problem, which local uniqueness stability are...