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Volume 14, Issue 2
Blow Up in a Semilinear Wave Equation

A. Messaoudi Salim

J. Part. Diff. Eq., 14 (2001), pp. 105-110.

Published online: 2001-05

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  • Abstract
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].
  • Keywords

Wave equation weak solutions negative energy blow up: finite time

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@Article{JPDE-14-105, author = {A. Messaoudi Salim }, title = {Blow Up in a Semilinear Wave Equation}, journal = {Journal of Partial Differential Equations}, year = {2001}, volume = {14}, number = {2}, pages = {105--110}, abstract = { 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].}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5473.html} }
TY - JOUR T1 - Blow Up in a Semilinear Wave Equation AU - A. Messaoudi Salim 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].
A. Messaoudi Salim . (2001). Blow Up in a Semilinear Wave Equation. Journal of Partial Differential Equations. 14 (2). 105-110. doi:
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