TY - JOUR

T1 - DEGENERATE HYPERBOLIC EQUATIONS WITH UNKNOWN DISSIPATION COEFFICIENT

AU - Kozhanov, A. I.

AU - Pavlov, S. S.

N1 - Kozhanov, A.I., Pavlov, S.S. DEGENERATE HYPERBOLIC EQUATIONS WITH UNKNOWN DISSIPATION COEFFICIENT. J Math Sci 300, 42–54 (2026). https://doi.org/10.1007/s10958-026-08494-0 The work is supported by the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-02-2026-1329).

PY - 2026/5/26

Y1 - 2026/5/26

N2 - We study the problems of finding the functions u(x, t) and q(t) related by the equation ϕ(t)utt − Δu + q(t)ut = f(x, t), where Δ is the Laplace operator with respect to the variables x1, ..., xn. A peculiarity of this equation is that the function ϕ is nonnegative and can vanish on its domain. These problems fall into the category of inverse coefficient problems. We prove existence and uniqueness theorems for regular solutions — solutions that have all weak derivatives in the sobolev sense as required by the equation. Bibliography: 4 titles.

AB - We study the problems of finding the functions u(x, t) and q(t) related by the equation ϕ(t)utt − Δu + q(t)ut = f(x, t), where Δ is the Laplace operator with respect to the variables x1, ..., xn. A peculiarity of this equation is that the function ϕ is nonnegative and can vanish on its domain. These problems fall into the category of inverse coefficient problems. We prove existence and uniqueness theorems for regular solutions — solutions that have all weak derivatives in the sobolev sense as required by the equation. Bibliography: 4 titles.

UR - https://www.mendeley.com/catalogue/8a202cef-0eab-3139-9acd-574b21e292a2/

UR - https://www.scopus.com/pages/publications/105040245340

U2 - 10.1007/s10958-026-08494-0

DO - 10.1007/s10958-026-08494-0

M3 - Article

VL - 300

SP - 42

EP - 54

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 1

ER -