Determination of Initial Data in the Time-Fractional Pseudo-Hyperbolic Equation
Serikbaev D. Tokmagambetov N.
October 2024Multidisciplinary Digital Publishing Institute (MDPI)
Symmetry
2024#16Issue 10
We examine a time-fractional pseudo-hyperbolic equation involving positive operators. We explore the determination of initial velocity and perturbation. It is demonstrated that these initial inverse problems are ill posed. Additionally, we prove that under certain conditions, the inverse problems exhibit well-posedness properties. Our focus is on developing a theoretical framework for these initial inverse problems associated with time-fractional pseudo-hyperbolic equations, laying the groundwork for future studies on numerical algorithms to solve these problems. This investigation is crucial for understanding the fundamental behavior of the equations under various initial conditions and perturbations. By establishing a rigorous theoretical framework, we pave the way for future research to focus on practical numerical methods and simulations. Our results provide a deeper insight into the mathematical structure of time-fractional pseudo-hyperbolic equations, ensuring that future computational approaches are built on a solid theoretical foundation.
initial inverse problem , time-fractional pseudo-hyperbolic , weak solution
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Centre de Recerca Matematica Edifici C, Campus Bellaterra, Barcelona, 08193, Spain
Institute of Mathematics and Mathematical Modeling
Centre de Recerca Matematica Edifici C
10 лет помогаем публиковать статьи Международный издатель
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