Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario.Then, we discuss the global existence of the solutions under certain conditions.After that, on condition that the compactly supported initial data keeps itssign, we prove the infinite propagation speed of our solutions, and establishthe large time behavior. Finally, we also elaborate the persistence property ofour solutions in weighted Sobolev space.