TITLE

Non-classical symmetries and similarity solutions for 2D nonlinear heat equation

AUTHOR(S)
Cimpoiasu, Rodica; Constantinescu, Radu
PUB. DATE
November 2013
SOURCE
AIP Conference Proceedings;Nov2013, Vol. 1564 Issue 1, p33
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This paper extends the new algorithm [8] for finding non-classical symmetries of dynamical systems described by partial differential equations. A distinct case is added to the original procedure. This general technique is applied to the 2D nonlinear heat equation for which classical symmetries are determined by [10]. New non-classical symmetry operators, different from the classical ones, are thus derived and by using them, some new similarity solutions for the analyzed model are pointed out.
ACCESSION #
91945231

 

Related Articles

  • A weighted inpainting algorithm based on TV model. Xiaoyun Wang; Zhihui Gao; Xianquan Zhang; Chunqiang Yu; Bin Ni; Feng Ding // International Journal of Digital Content Technology & its Applic;Jun2012, Vol. 6 Issue 11, p297 

    In this paper, we propose a fast algorithm based on the well known total variation (TV) inpainting model. In order to increase the proportion of useful information in the calculation and accelerate the spread of useful information, we endow pixels in the known areas and damaged areas with...

  • Analytic Approximation of Time-Fractional Diffusion-Wave Equation Based on Connection of Fractional and Ordinary Calculus. FALLAHGOUL, H.; HASHEMIPARAST, S. M. // Journal of Computational Analysis & Applications;Jan2013, Vol. 15 Issue 1, p1430 

    In this paper, we present a connection between fractional and ordinary derivative, which can be used in various fields of science and engineering deal with dynamical systems for solving fractional ordinary and partial differential equations. Some examples are given to show ability of the method...

  • The Self–similar Solution to Some Nonlinear Integro–differential Equations Corresponding to Fractional Order Time Derivative. Chang Miao; Han Yang // Acta Mathematica Sinica;Dec2005, Vol. 21 Issue 6, p1337 

    In this paper we study the self–similar solution to a class of nonlinear integro–differential equations which correspond to fractional order time derivative and interpolate nonlinear heat and wave equation. Using the space–time estimates which were established by Hirata and...

  • On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields. Goyal, Nisha; Gupta, R. K. // World Academy of Science, Engineering & Technology;2012, Issue 68, p610 

    Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the...

  • Symmetries, the current function, and exact solutions for Broadwell's two-dimensional stationary kinetic model. Ilyin, O. // Theoretical & Mathematical Physics;Jun2014, Vol. 179 Issue 3, p679 

    We investigate the Broadwell stationary kinetic model for four velocities on a plane using the current function that satisfies a partial differential equation. For this equation, we evaluate the algebras of classical and nonclassical symmetries and then construct invariant solutions. All classes...

  • Combined Nodal Method and Finite Volume Method for Flow in Porous Media. Elakkad, Abdeslam; Elkhalfi, Ahmed; Guessous, Najib // Wireless Sensor Network;Mar2010, Vol. 2 Issue 3, p227 

    This paper describes a numerical solution for two dimensional partial differential equations modeling (or arising from) a fluid flow and transport phenomena. The diffusion equation is discretized by the Nodal methods. The saturation equation is solved by a finite volume method. We start with...

  • THE ONE-DIMENSIONAL HEAT EQUATION AS A FIRST-ORDER SYSTEM: FORMAL SOLUTIONS BY MEANS OF THE LAPLACE TRANSFORM. TOPARKUS, HEINZ // Bulletin of Mathematical Analysis & Applications;2012, Vol. 4 Issue 2, p174 

    In this paper an extended heat equation problem as a linear first-order system of partial differential equations is considered. The classical problems in a strip S are assigned to our problems. Formal solutions are given by one-dimensional Laplace transform.

  • ON THE FORMATION OF SINGULARITIES FOR SURFACE WATER WAVES. Hur, Vera Mikyoung // Communications on Pure & Applied Analysis;Jul2012, Vol. 11 Issue 4, p1465 

    A Burgers equation with fractional dispersion is proposed to model waves on the moving surface of a two-dimensional, infinitely deep water under the influence of gravity. For a certain class of initial data, the solution is shown to blow up in finite time.

  • THE 2-COMPONENT DISPERSIONLESS BURGERS EQUATION ARISING IN THE MODELLING OF BLOOD FLOW. Lyons, Tony // Communications on Pure & Applied Analysis;Jul2012, Vol. 11 Issue 4, p1569 

    This article investigates the properties of the solutions of the dis-persionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well as applications of the model to clinical conditions.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics