Geodesic
Initial-boundary value problems for degenerate hyperbolic equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 43-53

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The aim of the paper is to study solvability in Sobolev spaces initial–boundary value problems for differential equations $$u_{tt}-\varphi(t)Au+c(x,t)u=f(x,t)$$ in which $A$ is an elliptic operator acting in the spatial variables $x_1$,\ldots,$x_n$ and $\varphi(t)$ is a non-negative function on the segment $[0,T]$. Existence theorems of regular solutions are proven. Some generalizations of the results are also described.
Keywords: hyperbolic equations, degeneration, initial-boundary value problems, regular solutions
Mots-clés : existence. 
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     author = {A. I. Kozhanov},
     title = {Initial-boundary value problems for degenerate hyperbolic equations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {43--53},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a22/}
}
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A. I. Kozhanov. Initial-boundary value problems for degenerate hyperbolic equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 43-53. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a22/