TY - JOUR
T1 - Blow Up in a Semilinear Wave Equation
JO - Journal of Partial Differential Equations
VL - 2
SP - 105
EP - 110
PY - 2001
DA - 2001/05
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5473.html
KW - Wave equation
KW - weak solutions
KW - negative energy
KW - blow up: finite time
AB -  We consider a semilinear wave equation of the form u_tt(x, t) - Δu(x, t) = - m(x, t)u_t(x, t) + ∇Φ(x) ⋅ ∇u(x, t ) + b(x)|u(x, t)|^{p-2}u(x, t) where p > 2. We show, under suitable conditions on m, Φ, b, that weak solutions break down in finite time if the initial energy is negative. This result improves an earlier one by the author [1].