Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A weak maximum principle-based approach for input-to-state stability
  analysis of nonlinear parabolic PDEs with boundary disturbances   In this paper, we introduce a weak maximum principle-based approach to
input-to-state stability (ISS) analysis for certain nonlinear partial
differential equations (PDEs) with boundary disturbances. Based on the weak
maximum principle, a classical result on the maximum estimate of solutions to
linear parabolic PDEs has been extended, which enables the ISS analysis for
certain {}{nonlinear} parabolic PDEs with boundary disturbances. To illustrate
the application of this method, we establish ISS estimates for a linear
reaction-diffusion PDE and a generalized Ginzburg-Landau equation with
{}{mixed} boundary disturbances. Compared to some existing methods, the scheme
proposed in this paper involves less intensive computations and can be applied
to the ISS analysis for a {wide} class of nonlinear PDEs with boundary
disturbances.

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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci