Physics Maths Engineering
Inverse problem for semilinear wave equation with strong damping
Related Subjects
Abstract
The initial-boundary and the inverse coefficient problems for the semilinear hyperbolic equation with strong damping are considered in this study. The conditions for the existence and uniqueness of solutions in Sobolev spaces to these problems have been established. The inverse problem involves determining the unknown time-dependent parameter in the right-hand side function of the equation using an additional integral type overdetermination condition.
Key Questions about Inverse Problems in Semilinear Wave Equations
The article "Inverse Problem for Semilinear Wave Equation with Strong Damping" by Nataliya Protsakh addresses the initial-boundary and inverse coefficient problems for semilinear hyperbolic equations exhibiting strong damping. The study establishes conditions for the existence and uniqueness of solutions within Sobolev spaces. The inverse problem focuses on determining an unknown time-dependent parameter in the equation's right-hand side function using an additional integral-type overdetermination condition. :contentReference[oaicite:4]{index=4}
1. What are the initial-boundary and inverse coefficient problems for semilinear hyperbolic equations with strong damping?
The article investigates these problems by establishing conditions for the existence and uniqueness of solutions in Sobolev spaces. :contentReference[oaicite:5]{index=5}
2. How can the unknown time-dependent parameter in the equation's right-hand side function be determined?
The study proposes using an additional integral-type overdetermination condition to determine this unknown parameter. :contentReference[oaicite:6]{index=6}
3. What methods are employed to prove the existence and uniqueness of solutions?
The author utilizes properties of solutions to the initial-boundary value problem and the method of successive approximations to establish these results. :contentReference[oaicite:7]{index=7}
