Related papers: General Solution to Unidimensional Hamilton-Jacobi…
We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms…
In this paper we apply the Fast Iterative Method (FIM) for solving general Hamilton-Jacobi-Bellman (HJB) equations and we compare the results with an accelerated version of the Fast Sweeping Method (FSM). We find that FIM can be indeed used…
In this study, the solution of the Hamilton-Jacobi equation (HJE) with holonomic Hamiltonian is investigated in terms of the first integrals of the corresponding Hamiltonian system. Holonomic functions are related to a specific type of…
This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…
In this paper, we generalized the known Laplace-transform final-value theorem. From our conclusion, one can deduce the existing results in [1, 3, 12]. By using final value theorem, we give a new proof that Caputo fractional differential…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
It is well known that a generic small perturbation of a Liouville-integrable Hamiltonian system causes breakup of resonant and near-resonant invariant tori. A general approach to the simple resonance case in the convex real-analytic setting…
The Adomian decomposition method is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The aim of this paper is to apply Adomian decomposition method to obtain approximate solutions of nonlinear…
In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…
A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding…
It is shown that, by appropriately defining the eigenfunctions of a function defined on the extended phase space, the Liouville theorem on solutions of the Hamilton--Jacobi equation can be formulated as the problem of finding common…
In this note a generalization of the Lamb-Bateman integral equation is presented and its solution is given in terms of {\bf fractional derivatives}. This is a comment one to the paper by Babusci, Dattoli and Sacchetti (arXiv:1006.0184…
Einstein equations for several matter sources in Robertson-Walker and Bianchi I type metrics, are shown to reduce to a kind of second order nonlinear ordinary differential equation $\ddot{y}+\alpha f(y)\dot{y}+\beta f(y)\int{f(y) dy}+\gamma…
We provide a review of some symmetry-related literature on the eikonal equations $u_\mu u_\mu =0$,$u_\mu u_\mu =1$, where lower indices at dependent variables designate derivatives, $\mu=0,1,2,..,n$ and summation is implied over the…
The solution of Kardar-Parisi-Zhang equation (KPZ equation) is solved formally via Cole-Hopf transformation $h=\log u$, where $u$ is the solution of multiplicative stochastic heat equation(SHE). In earlier works by Chatterjee and Dunlap,…
Our goal is to establish existence with suitable initial data of solutions to general parabolic equation in one dimension, $u_t = L(u_x)_x$, where $L$ is merely a monotone function. We also expose the basic properties of solutions,…
It is shown that extreme problem for one-dimensional Euler-Lagrange variational functional in $C^1[a;b]$ under the strengthened Legendre condition can be solved without using Hamilton-Jacobi equation. In this case, exactly one of the two…
In many mathematical types of research, in order to solve the fuzzy fractional differential equations, we should transform these problems into crisp corresponding problems and by solving them the approximate solution can be obtained. The…
In this work we obtain a Liouville theorem for positive, bounded solutions of the equation $$ (-\Delta)^s u= h(x_N)f(u) \quad \hbox{in }\mathbb{R}^{N} $$ where $(-\Delta)^s$ stands for the fractional Laplacian with $s\in (0,1)$, and the…
We consider in this note the Hamilton-Jacobi equation H(x, dx u) = c, where c \geq 0, of the classical N-body problem in an Euclidean space E of dimension k \geq 2. The fixed points of the Lax-Oleinik semigroup are global viscosity…