PreprintCC BY-NC-ND 4.0arXiv
The critical exponent for the two-dimensional semilinear wave equation with strong damping
Abstract
In this manuscript, we determine the critical exponent for the two-dimensional semilinear wave equation with strong damping. A recent result in D'Abbicco (arXiv, 2026) gives global in-time small data solutions for p>10/3, whereas we in the paper prove finite-time blow-up for 2<pleqslant10/3 under an averaged sign condition on the initial velocity. Together with the previously known blow-up result for 1<pleqslant3, the threshold for the power nonlinearity |u|p is p=pcrit=10/3. We prove positivity of the full two-dimensional velocity fundamental solution and construct a positive averaged kernel, which allows us to establish a nonlinear lower-bound iteration in a parabolic region.
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BibTeX
@misc{chen2026critical,
title = {{The critical exponent for the two-dimensional semilinear wave equation with strong damping}},
author = {Wenhui Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01964},
eprint = {2609.01964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01964},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The critical exponent for the two-dimensional semilinear wave equation with strong damping
AU - Wenhui Chen
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.01964
UR - https://arxiv.org/abs/2609.01964
AB - In this manuscript, we determine the critical exponent for the two-dimensional semilinear wave equation with strong damping. A recent result in D'Abbicco (arXiv, 2026) gives global in-time small data solutions for p>10/3, whereas we in the paper prove finite-time blow-up for 2<pleqslant10/3 under an averaged sign condition on the initial velocity. Together with the previously known blow-up result for 1<pleqslant3, the threshold for the power nonlinearity |u|^p is p=p_crit=10/3. We prove positivity of the full two-dimensional velocity fundamental solution and construct a positive averaged kernel, which allows us to establish a nonlinear lower-bound iteration in a parabolic region.
ER -