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We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasi-steady version of it. This simplification allows, near the planar front, an explicit derivation of the front equation. The latter is a pseudodifferential fully nonlinear parabolic equation of the fourth-order. First, we study the (orbital) stability of the null solution. Second, introducing a parameter $epsilon$, we rescale both the dependent and independent variables and prove rigourously the convergence to the solution of the Kuramoto-Sivashinsky equation as $epsilonto 0$.
The present article investigates the interactions between the pilot and main flames in a novel stratified swirl burner using both experimental and numerical methods. Experiments are conducted in a test rig operating at atmospheric conditions. The sys
In this paper we consider a class of fully nonlinear equations which cover the equation introduced by S. Donaldson a decade ago and the equation introduced by Gursky-Streets recently. We solve the equation with uniform weak $C^2$ estimates, which hold for degenerate case.
Entire solutions of the $n-$Laplace Liouville equation in $mathbb{R}^n$ with finite mass are completely classified.
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.
We consider the Schrodinger equation with nonlinear dissipation begin{equation*} i partial _t u +Delta u=lambda|u|^{alpha}u end{equation*} in ${mathbb R}^N $, $Ngeq1$, where $lambdain {mathbb C} $ with $Imlambda<0$. Assuming $frac {2} {N+2}<alpha<fra