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\} 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.
@article{7475,
title = {Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition - doi: 10.5269/bspm.v22i2.7475},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v22i2.7475},
language = {EN},
url = {http://dml.mathdoc.fr/item/7475}
}
Kirane, Mokhtar; NABANA, Eric; Pohozaev, Stanislav I. Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition - doi: 10.5269/bspm.v22i2.7475. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v22i2.7475. http://gdmltest.u-ga.fr/item/7475/