Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence

2001/02/09 by Daniel ben‐Avraham, Daniel ben-Avraham, A. S. Fokas +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.64.016114

published as Physical Review E 64, 016114 (2001). · RevTeX, 7 pages, 3 figures

arxiv created 2001/02/09 · openalex publication_date 2001/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q_xx(x,y)+q_yy(x,y)\ensuremath-4\ensuremathβ²q(x,y)=0 in the triangular domain 0<~x<~L\ensuremath-y<~L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A\ensuremath\rightleftharpoonsA, in the segment (\ensuremath-L/2,L/2), with traps at the edges.

Citations

• Complete Exact Solution of Diffusion-Limited Coalescence,A<mml:mspace/>+<mml:mspace/>A<mml:mspace/>→<mml:mspace/>A

Cited by

• The basic elliptic equations in an equilateral triangle