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The stationary problem of Problem (3.1) is as follows: (3.2).
The problem (1.1) is related to the stationary problem of a model introduced by Kirchhoff [5].
To understand the dynamics of system (1.4), we first consider its stationary problem in this paper.
We first consider the stationary problem of Problem (1.1) as follows: (4.1).
Problem (1.1) is related to the stationary problem introduced by Kirchhoff in [1].
We describe the numerical stationary problem and the linear stability analysis of the stationary solutions.
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Let be a nonnegative sub-solution to the stationary problems of Problem (1.1).
Finally we perform several numerical simulations for time evolution and stationary problems.
Many optimisation problems are dynamic in the sense that changes occur during the optimisation process, and therefore are more challenging than the stationary problems.
Common techniques for solving the flow equations in both time dependent and stationary problems are ray tracing and level set methods.
Additionally, the PIC-MCC method guarantees high accuracy for both transient and stationary problems [15], and yields more detailed information about the evolution of the discharge.
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