<b>Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition</b> - doi: 10.5269/bspm.v22i2.7475

Abstract

We consider the equation \Deltau = 0 posed in Q := (0;+\infty) \times \Omega ­;­ \Omega:=\{x = (x'; x_ N)/ x' \in  R^{N-1}; x_N > 0\}; with the dynamical boundary condition
B(t, x',0)u_{tt} + A(t, x',0)u_t - u_{x_N} \geq D(t; x',0; 0) |u|^q on \Sigma := (0;\infty) \times R^{N-1} \times \{0\} and give conditions on the coefficient functions A(t, x',0); B(t, x',0; 0) and D(t, x'; 0) for the nonexistence of global solutions.