We discuss the notions of resurgence, formalizability, and formation of singularities in the context of partial differential equations. The results show that Écalle’s how analyzability theory extends naturally to PDEs.

The mathematical modeling of a Pressure Swing Adsorption (PSA) system is discussed in detail for the Skarstrom cycle of two-bed process. The system is used to get pure oxygen product from the air with the use of zeolite 13X as an adsorbent. There are complex partial differential equations (pdes) which may not solve by analytical methods. There is no provision for solving it in any other softwar...

The connection of curves and surfaces in R3 to some nonlinear partial differential equations is very well known in differential geometry [1], [2]. Motion of curves on two dimensional surfaces in differential geometry lead to some integrable nonlinear differential equations such as nonlinear Schrödinger (NLS) equation [3], Korteweg de Vries (KdV) and modified Korteweg de Vries (mKdV) equations [...

Abstract This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential equations (PDEs) by using an asymptotic expansion with deep learning-based algorithm. In particular, mathematical justification on is provided. Numerical examples Kolmogorov PDEs show effectiveness our method.

Lattice systems arise in many applications, for example, in chemical reaction theory, image processing, pattern recognition, material science, biology, electrical engineering, laser systems, and so forth. A lattice dynamical system LDS is an infinite system of ordinary differential equations lattice ODEs or of difference equations. In some cases, they arise from spatial discretizations of parti...

A method for symbolically computing conservation laws of nonlinear partial differential equations (PDEs) in multiple space dimensions is presented in the language of variational calculus and linear algebra. The steps of the method are illustrated using the ZakharovKuznetsov and Kadomtsev-Petviashvili equations as examples. The method is algorithmic and has been implemented in Mathematica. The s...

The purpose of this work is to perform group classification a coupled system partial differential equations (PDEs) modeling flow in collapsible tubes. This PDEs contains unknown functions the dependent variables whose forms are specified via with respect subalgebras real three and four-dimensional Lie algebras.

Abstract We show the continuous dependence of solutions linear nonautonomous second-order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in weak-* topology is required. results important applications theory Lyapunov exponents to investigation PDEs

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the a...