Jesús Ildefonso Díıaz
To the memory of Haim Brezis: my adviser, my master, my friend
Abstract. We prove that the solutions of the damped Klein-Gordon equation with a monotone perturbation cannot fulfill the finite extinction time property, even if the perturbation is a non-Lipschitz (or multivalued) function of the unknown u. This contrasts with the case of the nonlinear Schrödinger damped equation (recent results dealing with this same monotone expressions but with a purely imaginary coefficient), and with the case of nonlinear parabolic equations with strong absorption (for which the finite extinction time property is well-known since the middle of the seventies of the last century).
Keywords: Damped semilinear Klein-Gordon equation, exponential decay, finite-time extinction, saturation nonlinear term, strong absorption.
MSC: 35L71, 81Q05, 37L05, 35B35.
DOI 10.56082/annalsarscimath.2025.1.297
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics on Its Application, Volume 17 no 1, 2025
