Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition
Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition
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 conditionB(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\} …