Abstract
We consider the initial-boundary value problem for a dissipative nonlinear wave equation of the Sobolev type with a nonlocal cubic source. For this problem we obtain a sufficient condition for blowup of a strong generalized solution. Moreover, we obtain a two-sided estimate for the blowup time of the solution.
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Original Russian Text Copyright © 2005 Korpusov M. O. and Sveshnikov A. G.
The authors were supported by the Russian Foundation for Basic Research (Grants 02-01-00253; 02-01-06038) and a grant of the Project “Junior Scientists of Russia.”
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 567–578, May–June, 2005.
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Korpusov, M.O., Sveshnikov, A.G. On Blowup of a Solution to a Sobolev-Type Equation with a Nonlocal Source. Sib Math J 46, 443–452 (2005). https://doi.org/10.1007/s11202-005-0047-5
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DOI: https://doi.org/10.1007/s11202-005-0047-5