Related papers: Non-Linear Evolution Equations with Non-Analytic D…
Blowup analysis for solutions of a general evolution equation with nonlocal diffusion and localized source is performed. By comparison with recent results on global-in-time solutions, a dichotomy result is obtained.
In this paper the Singular Manifold Method has allowed us to obtain the Lax pair, Darboux transformations and tau functions for a non-linear Schr\"odiger equation in 2+1 dimensions. In this way we can iteratively build different kind of…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.
In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…
We address the problem of classification of integrable differential-difference equations in 2+1 dimensions with one/two discrete variables. Our approach is based on the method of hydrodynamic reductions and its generalisation to dispersive…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…
In this paper it is dealt with the following system of difference equations x_{n+1}=((a_{n})/(x_{n}))+((b_{n})/(y_{n})), y_{n+1}=((c_{n})/(x_{n}))+((d_{n})/(y_{n})), n in N_0, where the initial values x_0,y_0 are positive real numbers and…
For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The results are valid for large deformations and essentially…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal…
We expand the class of linear symmetric equations for which large sets with no non-trivial solutions are known. Our idea is based on first finding a small set with no solutions and then enlarging it to arbitrary size using a…
We obtain new $L^1$ contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or non-local diffusion terms. As opposed to…
he Singular Manifold Method is presented as an excellent tool to study a 2+1 dimensional equation in despite of the fact that the same method presents several problems when applied to 1+1 reductions of the same equation. Nevertheless these…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
We collect evidence that the notion of path-ordered non-abelian integration admits an extension to two dimensions. We propose the corresponding notion of non-abelian 2-form along the lines of Lie algebroid theory and argue it is an…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
In this work we construct a variety of new complex-valued proper biharmonic maps and (2,1)-harmonic morphisms on Riemannian manifolds with non-trivial geometry. These are solutions to a non-linear system of partial differential equations…
The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, optimization. In the paper, we derive some new results for…