The July 2005 AMWS Newsletter included an article on the Identification and Control of Invasive Knotweeds by Timothy W. Miller, Ph.D., a professor at Washington State University. The article is excellent and you should try to obtain a copy if you can.
He indicated that controlling these species is difficult. Be patient. The article discusses mowing and the use of various herbicides, including foliar application and injection of herbicide into the hollow stem of the plant. As with all herbicides, they must be used in accordance with label directions and the like.
Dr. Miller's contact information listed in the article is firstname.lastname@example.org