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We would like to assure that Equations (1.1) and (1.2) are a nontrivial generalization of the corresponding problems with (r = 1).
Obviously, the Neumann boundary value conditions will cause some additional difficulties in establishing the a priori estimates (see for instance [26, 28]), which will be the topic of our further work in the future as well as the corresponding problems with Dirichlet-Neumann boundary conditions.
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There has never been a greater need for critical engagement with the role technology plays in society, but there's a corresponding problem with that engagement, as severe now as it was when CP Snow diagnosed it in 1959: the lack of understanding between the sciences and the humanities.
Deblending and dictionary learning with l1-norm based sparsity are combined to construct the corresponding problem with respect to unknown recovery, dictionary, and coefficient sets.
By studying the corresponding problem with initial condition t = h, then passing to the limits h → − ∞, we obtained the existence and uniqueness of the solution.
Then we construct an actual solution to the corresponding problem with the analytic continuation of this κ-sum as non-homogeneous term, within the Banach spaces defined in Section 2.
Using the Faedo-Galerkin method in [18] it is proved that the corresponding problem with homogeneous boundary conditions for velocity, microrotation and heat flux has a generalized solution locally in time, i.e. on the domain (]0,1[,times,]0,T_{0}[), where (T_{0}>0) is sufficiently small. In [19] the uniqueness of the generalized solution for the same problem is proved.
We first consider the corresponding problem with the linear equation begin{aligned} left { textstylebegin{array}l} u_{t}+L_{p}u_{t}+u_{x}+M_{alpha}u=0,quad xinmathbb {T}, tin 0,T), u 0,x =u_{0}(x),quad xinmathbb{T}, int_{mathbb{T}}u t,x),dx=0.
The subset S consists of all solutions of corresponding problems (1 - 2) with non-negative f.
Therefore, we have to transform near defective systems into the defective one, and then modal optimal control procedure for the defective systems can be extended to deal with the corresponding problems for near defective systems with close eigenvalues.
However, to the best of our knowledge, very little has been done with the corresponding problems for impulsive delay difference equations with continuous variables.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com