Fixing EFT equations with a reservoir model

Effective Field Theories with higher derivatives often yield equations of motion which define ill-posed problems. We present a method for enhancing control on such theories by coupling them to a field living in one extra dimension. The resulting action principle helps to define a well-posed problem introducing a mechanism to control UV behavior. Physically this is achieved by dissipating the energy in the short-wavelength modes into the extra dimension. We examine the resulting dynamics and compare it to alternative proposals for studying such theories in the non-linear regime.