Some qualitative properties of solutions of a generalised diffusion equation

Publisher Website
Google Scholar
Abstract
Atkinson and Peletier (2,3) have considered similarity solutions of the differential equation where the function k(s) is defined, real and continuous for s ≥ 0 and k(s) > 0 if s > 0 (in (2) k(0) = 0 is also assumed). In particular they look for similarity solutions of the form u(x, t) = f(η) where η = x(t+l)−½ with boundary conditions f(0) = A and . They show that if k(s) satisfies the condition then for any A > 0 there is a unique similarity solution which is non-negative and has compact support in [0, ∞). They also show in (2) that is a necessary condition for the solution to have compact support. In (3) they prove existence of similarity solutions when and show that in this case the similarity solution has the property that f(η) > 0 for all η > 0.

This publication has 5 references indexed in Scilit: