Geodesic
Pseudoparabolic and pseudohyperbolic equations in noncylindrical time domains
Matematičeskie zametki SVFU, Tome 26 (2019) no. 3, pp. 15-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study solvability of new boundary value problems for pseudoparabolic and pseudohyperbolic equations with one spatial variable. The solutions for these problems are sought in domains noncylindrical along the time variable, not in the domains with curvilinear borders (domains with moving border) as in the previous works. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives, required in the equation, in the inner subdomains.
Mots-clés : pseudoparabolic equation, existence
Keywords: pseudohyperbolic equation, noncylindrical domain, boundary value problem, regular solution, uniqueness. 
@article{SVFU_2019_26_3_a1,
     author = {A. I. Kozhanov and G. A. Lukina},
     title = {Pseudoparabolic and pseudohyperbolic equations in noncylindrical time domains},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {15--30},
     year = {2019},
     volume = {26},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2019_26_3_a1/}
}
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A. I. Kozhanov; G. A. Lukina. Pseudoparabolic and pseudohyperbolic equations in noncylindrical time domains. Matematičeskie zametki SVFU, Tome 26 (2019) no. 3, pp. 15-30. http://geodesic.mathdoc.fr/item/SVFU_2019_26_3_a1/