For a class of semilinear parabolic equations under nonlinear dynamical boundary conditions in a bounded domain, we obtain finite time blow-up solutions when the initial data varies in the phase space $ H_0^1(\Omega) $ at positive initial energy level and get global solutions with the initial data at low and critical energy level. Our main tools are potential well method and concavity method.
Citation: Mingyou Zhang, Qingsong Zhao, Yu Liu, Wenke Li. Finite time blow-up and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition[J]. Electronic Research Archive, 2020, 28(1): 369-381. doi: 10.3934/era.2020021
For a class of semilinear parabolic equations under nonlinear dynamical boundary conditions in a bounded domain, we obtain finite time blow-up solutions when the initial data varies in the phase space $ H_0^1(\Omega) $ at positive initial energy level and get global solutions with the initial data at low and critical energy level. Our main tools are potential well method and concavity method.
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Mingyou Zhang, Qingsong Zhao, Yu Liu, Wenke Li. Finite time blow-up and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition[J]. Electronic Research Archive, 2020, 28(1): 369-381. doi: 10.3934/era.2020021
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