Geodesic
Integral Analogue of the First Initial-Boundary Value Problem for Second-Order Hyperbolic and Parabolic Equations
Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 540-550

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We study the solvability of initial-boundary value problems for second-order hyperbolic and parabolic equations with a boundary condition that integrally connects the values of the solution on the lateral boundary with the values of the solution inside the domain. To study such problems, it was previously established that their solvability is ensured by the bijectivity of a certain Fredholm operator constructed from an integral condition. In this paper, we show that the condition of predecessors is not required for the existence and uniqueness of regular solutions (solutions with all derivatives generalized in the sense of Sobolev that are contained in the equation) of integral analogues of the first initial-boundary value problem for second-order hyperbolic and parabolic equations.
Keywords: second-order hyperbolic and parabolic equations, nonlocal problems, integral analogue of the first initial-boundary value problem, regular solutions, uniqueness.
Mots-clés : existence 
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     author = {A. I. Kozhanov and A. V. Dyuzheva},
     title = {Integral {Analogue} of the {First} {Initial-Boundary} {Value} {Problem} for {Second-Order} {Hyperbolic} and {Parabolic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {111},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a5/}
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A. I. Kozhanov; A. V. Dyuzheva. Integral Analogue of the First Initial-Boundary Value Problem for Second-Order Hyperbolic and Parabolic Equations. Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 540-550. http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a5/