Blow-up problems for a parabolic equation coupled with superlinear source and local linear boundary dissipation
arXiv:2201.08961 · doi:10.1016/j.jmaa.2022.126327
Abstract
In this paper, we consider the finite time blow-up results for a parabolic equation coupled with superlinear source term and local linear boundary dissipation. Using a concavity argument, we derive the sufficient conditions for the solutions to blow up in finite time. In particular, we obtain the existence of finite time blow-up solutions with arbitrary high initial energy. We also derive the upper bound and lower bound of the blow up time.
in press on Journal of Mathematical Analysis and Applications, see https://www.sciencedirect.com/science/article/pii/S0022247X22003419