Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc