Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear evolution equations with exponentially decaying memory:
  Existence via time discretisation, uniqueness, and stability   The initial value problem for an evolution equation of type $v' + Av + BKv =
f$ is studied, where $A:V_A \to V_A'$ is a monotone, coercive operator and
where $B:V_B \to V_B'$ induces an inner product. The Banach space $V_A$ is not
required to be embedded in $V_B$ or vice versa. The operator $K$ incorporates a
Volterra integral operator in time of convolution type with an exponentially
decaying kernel. Existence of a global-in-time solution is shown by proving
convergence of a suitable time discretisation. Moreover, uniqueness as well as
stability results are proved. Appropriate integration-by-parts formulae are a
key ingredient for the analysis.

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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs