Hi. Japanese Knotweed is challenging to control, but it can be done. Ohio State University’s Buckeye Yard and Garden Online newsletter had a nice post on it a few years ago, and you can read it here. It refers to an excellent fact sheet from the U. of Michigan (accessible here). Penn State also has an excellent article on Japanese knotweed that you can read here. All of those articles note that the key to controlling knotweed is eliminating the rhizomes (underground stems), since new plants can sprout even from small pieces. Eliminating rhizomes requires chemical control over several years, typically in combination with mechanical control (e.g., cutting). The U. of Michigan fact sheet recommends the herbicide imazapyr, but the Penn State article notes that this can injure nearby trees through root uptake. Penn State recommends glyphosate, which the U. of Michigan says is less effective than imazapyr. Which you use will partly depend on the site and the proximity of other species. Both herbicides are non-selective, which means they will affect any plant with which they come in contact. The Penn State article provides a calendar for timing of glyphosate applications to maximize effectiveness. If you decide to use an herbicide, be sure to carefully read the label and follow the label directions. Good luck!