Tue, September 10, 2024
10:20 am - 11:20 am
Math Tower (MW) 154
Timur Akhunov
Wabash College
Title
Modified energy method for illposedness of dispersive equations
Abstract
Korteweg and de Vries in 1890s derived an equation that bears their name to elucidate unusual behavior of water waves. They discovered solitons that behave like billiard balls when interacting. Can solitons be made compactly supported? Rosenau-Hyman in 93 proposed partial differential equations with such solutions that they dubbed “compactons”. Wellposedness of compacton equations is poorly understood. A plausible avenue to prove illposedness results is a modified energy method.