Geodesic
Initial-boundary value problem for hyperbolic equations with an arbitrary order elliptic operator
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 30 (2020) no. 1, pp. 8-19

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An initial-boundary value problem for a hyperbolic equation with the most general elliptic differential operator, defined on an arbitrary bounded domain, is considered. Uniqueness, existence and stability of the classical solution of the posed problem are proved by the classical Fourier method. Sufficient conditions for the initial function and for the right-hand side of the equation are indicated, under which the corresponding Fourier series converge absolutely and uniformly. The notion of a generalized solution is introduced and existence theorem is proved. Similar results are formulated for parabolic equations too.
Keywords: hyperbolic equation, initial-boundary value problems, Fourier method, uniqueness, stability, classical solution, generalized solution.
Mots-clés : existence 
@article{VKAM_2020_30_1_a0,
     author = {R. R. Ashurov and A. T. Muhiddinova},
     title = {Initial-boundary value problem for hyperbolic equations with an arbitrary order elliptic operator},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {8--19},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2020_30_1_a0/}
}
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R. R. Ashurov; A. T. Muhiddinova. Initial-boundary value problem for hyperbolic equations with an arbitrary order elliptic operator. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 30 (2020) no. 1, pp. 8-19. http://geodesic.mathdoc.fr/item/VKAM_2020_30_1_a0/