### Electronic Research Archive

2020, Issue 1: 369-381. doi: 10.3934/era.2020021
Special Issues

# Finite time blow-up and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition

• Primary: 35K58; Secondary: 35K60

• 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

### Related Papers:

• 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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