In this paper, we adopt the K-best solution with fixed complexity as the basic solution of the SD.
In part 1, we deduce the exponential stability of the basic solution of the homogeneous equation of (2.1), and in part 2, we employ the fixed point principle to discuss the case of the nonhomogeneous equation.
In Section 3, based on the basic solution of the definite homogeneous fourth-order parabolic equation, by applying the fixed point theory we prove the existence, uniqueness, and pth moment exponential stability of hybrid stochastic fourth-order parabolic equations.
In this section, we will first deduce the exponential stability of the basic solution of the homogeneous equation of (2.1), and then we will use the fixed point principle to discuss the existence and uniqueness of the mild solution to (2.1) and prove the exponential stability results.
One difficulty is related to the basic solution of the physical flow equations and involves choosing appropriate nonlocal open boundary conditions at the outflow boundaries which will adequately bound the computational domain while providing information about the virtual flow behavior outside.
The LPT and SPT strategies are considered by Lamiri et al. as a constructive heuristic in order to calculate a basic solution of the planning problem [ 23].
One of the basic solutions of such problem is to switch the idle mode server to either sleep mode or off mode based on resource demands, that leads to great energy saving because idle mode server consumes 70% of their peak power [13].
In this paper, the basic solutions of two parallel mode-I cracks or four parallel mode-I cracks in the piezoelectric materials were investigated by means of the Schmidt method for the limited-permeable electric boundary conditions.
Exposure of these paint films to neutral to basic solutions of low conductivity such as the DI water used here is known to promote swelling and hence the mobility of additives, such as surfactants [22].
To investigate the effect of the basic solution on the morphology of the obtained materials, the morphologies of the synthesized materials were studied by field emission scanning electron microscopy technique.
