A non-local parabolic equation modelling linear friction welding is studied. The equation applies on the half line and contains a non-linearity of the form f(u)/(?08 f(u)dy)1+a. For f(u) = eu, global existence and convergence to a steady state are proved. Numerical calculations are also carried out for this case and for f(u) = (-u)1/a. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
- Non-local parabolic problems