The Solution of the Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-Limited Coalescence
Abstract
A new transform method for solving boundary value problems for linear and integrable nonlinear PDEs recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation qxx(x,y)+qyy(x,y)-4b2q(x,y)=0 in the triangular domain 0 < x < L-y < L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A + A <--> A, in the segment (-L/2,L/2), with traps at the edges.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.