Premium
Finite time blow‐up for a kind of initial‐boundary value problem of semilinear damped wave equation
Author(s) -
Lai Ningan,
Yin Silu
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4046
Subject(s) - mathematics , wave equation , boundary value problem , mathematical analysis , initial value problem , domain (mathematical analysis) , argument (complex analysis) , power (physics) , contradiction , function (biology) , boundary (topology) , physics , biochemistry , chemistry , quantum mechanics , evolutionary biology , biology , philosophy , epistemology
In this paper, we consider the initial‐boundary value problem of semilinear damped wave equation u t t −Δ u + u t =| u | p with power p = 1 + 2 nin an exterior domain. Blow‐up result in a finite time will be established in higher dimensions ( n ≥3), no matter how small the initial data are. A special test function will be constructed, and then, we obtain the blow‐up result by a contradiction argument. Copyright © 2016 John Wiley & Sons, Ltd.