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Eurasian Mathematical Journal, 2014, Volume 5, Number 4, Pages 92–112
(Mi emj177)
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The Cauchy problem for one-dimensional wave equations with a nonlinear dissipative term
O. Jokhadze Department of Differential Equations, I. Javakhishvili Tbilisi State University, 2 University St., 0186, Tbilisi, Georgia
Abstract:
The Cauchy problem for one-dimensional wave equations with a nonlinear dissipative term is investigated. Under consideration are the problems of uniqueness and existence of local, global and blow-up solutions. The paper's originality is the coalescence of the two standard methods: a priori estimate of solutions in the class of continuous functions is given by energetic methods; basing on this result a priori estimate in the class of continuously differentiable functions using classical method of characteristics is obtained.
Keywords and phrases:
Cauchy problem, a priori estimate, wave equations with a nonlinear dissipative term, local and global solvability, nonexistence of global solutions, blow-up solutions.
Received: 01.11.2013
Citation:
O. Jokhadze, “The Cauchy problem for one-dimensional wave equations with a nonlinear dissipative term”, Eurasian Math. J., 5:4 (2014), 92–112
Linking options:
https://www.mathnet.ru/eng/emj177 https://www.mathnet.ru/eng/emj/v5/i4/p92
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Abstract page: | 206 | Full-text PDF : | 98 | References: | 38 |
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