Topic
Graph equation
About: Graph equation is a research topic. Over the lifetime, 33 publications have been published within this topic receiving 164 citations.
Papers
1 Jan 2013
TL;DR: In this article, the analytical solution for the generalized time-fractional tele-graph equation was derived by taking the Laplace and Fourier transforms in variable tand xrespectively.
Abstract: We discuss and derive the analytical solution for the generalized time-fractional tele- graph equation. These problems are solved by taking the Laplace and Fourier transforms in variable tand xrespectively. Here we use Green function also to derive the solution of the given differential equation.
17 citations
Posted Content•
Abstract: We discuss the linearization of a non-autonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized symmetries which turn out to be non-autonomous and depending on an arbitrary function of the dependent variables defined in two lattice points. These generalized symmetries are differential difference equations which, in some case, admit peculiar Backlund transformations.
14 citations
TL;DR: In this article, the authors studied the minimal graph equation in a Riemannian manifold and showed that the foliation by the level hypersurfaces of a $p$-harmonic submersion is a minimal foliation with respect to a conformally deformed metric.
Abstract: We study the minimal graph equation in a Riemannian manifold. After explaining the geometric meaning of the solutions and giving some entire solutions of the minimal graph equation in Nil space and in a hyperbolic space we find a link among $p$-harmonicity, horizontal homothety, and the minimality of the vertical graphs of a submersion. We also study the transformation of the minimal graph equation under the conformal change of metrics. We prove that the foliation by the level hypersurfaces of a $p$-harmonic submersion is a minimal foliation with respect to a conformally deformed metric. This implies, in particular, that the graph of any harmonic function from a Euclidean space is a minimal hypersurface in a complete conformally flat space, thus providing an effective way to construct (foliations by) minimal hypersurfaces.
12 citations
TL;DR: In this paper, the linearization of a non-autonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube has been discussed.
Abstract: We discuss the linearization of a nonautonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized symmetries, which turn out to be nonautonomous and dependent on an arbitrary function of the dependent variables defined at two lattice points. These generalized symmetries are differential–difference equations, which admit peculiar Backlund transformations in some cases.
12 citations
Posted Content•
TL;DR: In this article, it was shown that the asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs, including the minimal graph equation, is not solvable.
Abstract: We show, by modifying Borb\'ely's example, that there are $3$-dimen\-sional Cartan-Hadamard manifolds $M$, with sectional curvatures $\le -1$, such that the asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs, including the minimal graph equation, is not solvable.
12 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 1 |
| 2019 | 2 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 4 |