2019/10/01 by Nguyen Huy Tuan, Tuan, Nguyen Huy, Tomás Caraballo +5 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1910.00326
openalex publication_date 2019/10/01 · openalex created_date 2019/10/18 · openalex updated_date 2026/07/28
We consider the terminal value problem (or called final value problem, initial inverse problem, backward in time problem) of determining the initial value, in a general class of time-fractional wave equations with Caputo derivative, from a given final value. We are concerned with the existence, regularity of solutions upon the terminal value. Under several assumptions on the nonlinearity, we address and show the well-posedness (namely, the existence, uniqueness, and continuous dependence) for the terminal value problem. Some regularity results for the mild solution and its derivatives of first and fractional orders are also derived. The effectiveness of our methods are showed by applying the results to two interesting models: Time fractional Ginzburg-Landau equation, and Time fractional Burgers equation, where time and spatial regularity estimates are obtained.