Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary Feedback Control of Complex Ginzburg-Landau Equation with A
  Simultaneously Space and Time Dependent Coefficient   Linearized complex Ginzburg-Landau equation models various physical phenomena
and the stability controls of them are important. In this paper, we study the
control of the LCGLE with a simultaneously space and time dependent coefficient
by transforming it into a complex heat equation. It is shown that under certain
conditions on the coefficient functions $a_2(\tilde{x},\tilde{t})$, the
exponential stability of the system at any rate can be achieved by boundary
control based on the state feedback. The kernels are {\it explicitly}
calculated as series of approximation and shown to be twice differentiable by
using the {\it method of dominant}. Both the exponential stabilities of the
systems with Dirichlet and Neumann boundary conditions are strictly proven.

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The categories of this paper are: comp-gas
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph