Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations
arxiv(2022)
摘要
Lying between traditional parabolic and hyperbolic equations, time-fractional
wave equations of order α∈(1,2) in time inherit both decaying and
oscillating properties. In this article, we establish a long-time asymptotic
estimate for homogeneous time-fractional wave equations, which readily implies
the strict positivity/negativity of the solution for t≫1 under some sign
conditions on initial values. As a direct application, we prove the uniqueness
for a related inverse source problem on determining the temporal component.
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关键词
related inverse source problem,estimate,long-time,time-fractional
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