Department of Mathematics, Georgetown University, Box 571233, Washington, DC 20057, USA
Copyright © 2010 Hans Engler. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The fractional reaction diffusion equation
is discussed, where is a fractional differential operator on of order
, the function vanishes at and , and either
on or near . In the case of nonnegative g,
it is shown that solutions with initial support on the positive half axis
spread into the left half axis with unbounded speed if satisfies some
weak growth condition near in the case , or if is merely
positive on a sufficiently large interval near in the case . On the other hand, it shown that solutions spread with finite speed if
. The proofs use comparison arguments and a suitable family
of travelling wave solutions.