Large-time behavior of smooth solutions to a nonuniformly parabolic equation

AbstractWe study the large-time behavior of smooth solutions to a nonuniformly parabolic equation with bounded initial data. Decay rates of the solution in Lp(p ϵ [1, ∞]) norm are obtained in Theorem 2.3. Meanwhile, we obtain that the solution converges to a self-similar solution only depending on the behavior of the initial data at infinity and convergence rates are also derived in Theorem 4.4. On the other hand, we also obtain periodic behavior of the solution under periodic initial data and exponential decay of the solution in L2 norm in Theorem 3.1. These results cover the conclusion in [1]