Stability estimate and the Tikhonov regularization method for the Kuramoto–Sivashinsky equation backward in time

Abstract In this paper, we study the Kuramoto–Sivashinsky (KS) equation backward in time. First, we prove a stability estimate of Hölder type. Then the ill-posed problem is regularized by the Tikhonov regularization method, and an error estimate of Hölder type is obtained. Finally, we apply a physics-informed neural network method to solve the problem numerically.