An Inverse Problem for the Wave Equation with a Power-Law Nonlinearity and a Potential Depending on Spatial and Temporal Variables

An Inverse Problem for the Wave Equation with a Power-Law Nonlinearity and a Potential Depending on Spatial and Temporal Variables Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2026, Volume: 36, Number: 4, Pages: 433-450 Pages count : 18 DOI: 10.1134/S1055134426040061

Funding (1)

Министерство науки и высшего образования РФ

FWNF-2026-0029

We consider the inverse problem on recovering the coefficient $q$ of the wave equation $\partial^2_t u-\partial^2_x u-qu^{\gamma+1}=0$ with $\gamma\ge0$ on $\mathbb{R}^{+}\times (0,T]$. We study properties of solutions to the direct problem and prove that there exists a unique solution. For the inverse problem, we prove that a solution locally exists and establish a global estimate for its stability.

Romanov V.G. , Bugueva T.V.
An Inverse Problem for the Wave Equation with a Power-Law Nonlinearity and a Potential Depending on Spatial and Temporal Variables
Siberian Advances in Mathematics. 2026. V.36. N4. P.433-450. DOI: 10.1134/S1055134426040061

Романов В.Г. , Бугуева Т.В.
Обратная задача для волнового уравнения со степенной нелинейностью и потенциалом, зависящим от пространственной и временной переменных
Математические труды. 2026. Т.29. №3. С.226-254. DOI: 10.25205/1560-750X-2026-29-3-226-254

Submitted:	May 14, 2026
Accepted:	Jun 28, 2026
Published print:	Aug 6, 2026

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