Large time behavior of weak solutions to the surface growth equation

This paper studies the existence and decay estimates of weak solutions to surface growth equation. First, global is obtained by approximation method introduced Majda Bertozzi [Vorticity Incompressible Flow (Cambridge University Press, 2001)]. Then, we derive L2-decay rates via Fourier splitting under assumption that u0∈L1(R)∩L2(R). For more general cases, i.e., u0∈L2(R), behavior in L2 spectral theory self-adjoint operators.