Geodesic
The Cauchy problem for one-dimensional wave equations with a~nonlinear dissipative term
Eurasian mathematical journal, Tome 5 (2014) no. 4, pp. 92-112

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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. 
@article{EMJ_2014_5_4_a6,
     author = {O. Jokhadze},
     title = {The {Cauchy} problem for one-dimensional wave equations with a~nonlinear dissipative term},
     journal = {Eurasian mathematical journal},
     pages = {92--112},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2014_5_4_a6/}
}
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O. Jokhadze. The Cauchy problem for one-dimensional wave equations with a~nonlinear dissipative term. Eurasian mathematical journal, Tome 5 (2014) no. 4, pp. 92-112. http://geodesic.mathdoc.fr/item/EMJ_2014_5_4_a6/