Related papers: Group classification of variable coefficient quasi…

We determine the fusion rules of the equivariantization of a fusion category $\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\mathcal{C}$ and group-theoretical data associated to the group action. As an…

The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schr\"odinger equations of the form…

Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations $u'=A(u)u+f(u)$ is established in a certain critical case of strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ for the domains…

van't Hoff equation relates equilibrium constant $K$ of a chemical reaction to temperature $T$. Though the van't Hoff plot ($\ln K$ vs $1/T$) is linear, it is nonlinear for certain chemical reactions. In this work we attribute such…

We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear pattern-forming reaction-diffusion-advection systems, close to the first instability. We present a simple theorem which is easily applicable for such…

In this paper we prove some general theorems about representations of finite groups arising from the inner semidirect product of groups. We show how these results can be used for standard applications of group theory in quantum chemistry…

The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems \[ - \mbox{div}\big(\epsilon^{2}\phi(\epsilon|\nabla u|)\nabla u\big) + V(x)\phi(| u|)u = f(u)\quad \mbox{in} \quad…

In this work we analyze the existence of solution to the fractional quasilinear problem, \begin{equation*} \left\{ \begin{array}{rcll} (-\Delta)^s u &= & |\nabla u|^{p}+ \l f & \text{ in }\Omega , u &=& 0 &\hbox{ in }…

We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equation $u_t = u_{xx} + f(u)$ with $f(0)=f(1)=0$, and $f>0$ in $(0,1)$, which permits, in principle, the calculation of the exact speed for…

We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up…

In this work we carry out a complete group classification of Burgers' equations.

This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…

The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…

A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear…

Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general…

Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…

In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…

We propose a new method for constructing exact solutions to nonlinear delay reaction--diffusion equations of the form $$ u_t=ku_{xx}+F(u,w), $$ where $u=u(x,t)$, $w=u(x,t-\tau)$, and $\tau$ is the delay time. The method is based on…

We consider the identification of nonlinear diffusion coefficients of the form $a(t,u)$ or $a(u)$ in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assumptions using…

In this paper, we extend some of the multilevel convergence results obtained by Xu and Zhu in [Xu and Zhu, M3AS 2008], to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners…