1 research outputs found
Existence and regularity results for terminal value problem for nonlinear fractional wave equations
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