The Solution of the Modified Helmholtz Equation in a Wedge and an Application to Diffusion-Limited Coalescence

Abstract

The general solution of the modified Helmholtz equation, q_{xx}(x,y)+q_{yy}(x,y)-4b^2q(x,y)=0, in the wedge 0 < x < y < infinity, is presented. This solution is used to find the explicit steady-state of diffusion-limited coalescence, A+A<-->A, on the half-line, with a trap-source at the origin.

References in corpus (4)

• Complete Exact Solution of Diffusion-Limited Coalescence, A + A -> A
• Inhomogeneous Steady States of Diffusion-Limited Coalescence, A+A<-->A
• Diffusion-Limited Coalescence, A+A<-->A, with a Trap
• Generalized von Smoluchowski model of reaction rates, with reacting particles and a mobile trap

Cited by in corpus (3)

• The Unified Method: I Non-Linearizable Problems on the Half-Line
• The Solution of the Modified Helmholtz Equation in a Triangular Domain and an Application to Diffusion-Limited Coalescence
• The Basic Elliptic Equations in an Equilateral Triangle