Conditions for the existence of a global strong solution to a class of nonlinear evolution equations in a Hilbert space

Otelbaev, M.; Durmagambetov, A. A.; Seitkulov, Yerzhan

doi:10.1134/s0081543808010148

Cited by 7 publications

(6 citation statements)

References 2 publications

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“…Here, we note that in applications, equations in an unbounded domain with unbounded coefficients at infinity often appear [1][2][3][9][10][11][12]15]. In this regard, there is a need to study the spectral and approximation properties of differential operators with unbounded coefficients.…”

Section: Discussionmentioning

confidence: 99%

“…The term "separability" was first used in the papers of W. Everitt and M. Giertz [9]. The papers [2,[9][10][11] and the articles cited there are devoted to the issues of separability of differential operators of elliptic, hyperbolic, and mixed types, given in an unbounded domain. In this paper, apparently for the first time, we present the separability of the operator of parabolic type.…”

Section: Definitionmentioning

confidence: 99%

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Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type

Muratbekov,

Igissinov

2023

Mathematics

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In this paper, we study a differential operator of parabolic type with a variable and unbounded coefficient, defined on an infinite strip. Sufficient conditions for the existence and compactness of the resolvent are established, and an estimate for the maximum regularity of solutions of the equation Lu=f∈L2(Ω) is obtained. Two-sided estimates for the distribution function of approximation numbers are obtained. As is known, estimates of approximation numbers show the rate of best approximation of the resolvent of an operator by finite-dimensional operators. The paper proves the assertion about the existence of positive eigenvalues among the eigenvalues of the given operator and finds two-sided estimates for them.

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Section: Discussionmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type

Muratbekov,

Igissinov

2023

Mathematics

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“…Now, we apply the localization method [11] to the operator

T

. Let

{normalΔ}_{j} = (j - 1, j + 1),

where

j

is integer.…”

Section: The Maximal Regularity Conditions In the Case ρ1=1mentioning

confidence: 99%

“…In the case that the coefficients

ρ_{1}

ρ_{2}

are constant, some correctness results for Equation () are given in [10]. For the first time, coercive estimates for differential equations with nonsmooth coefficients were obtained in [11].…”

Section: Introductionmentioning

confidence: 99%

The maximal regularity of the third‐order differential equation and its applications

Ospanov,

Ospanov

2024

Math Methods in App Sciences

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In this work, we study the solvability and maximal regularity questions for the singular third‐order differential equation with unbounded coefficients and some applications. Unlike previously studied cases, the leading and intermediate coefficients of this equation can grow independently. We obtain sufficient coefficient conditions for correctness of this equation and compactness for inverse of the corresponding differential operator. We also prove the maximal regularity estimate for a generalized solution. Using these results, we obtain upper and lower estimates for the number of Kolmogorov ‐diameters of the set associated with the linear Korteweg–de Vries equation's solutions. We give an example and show that from the above inequalities follow two‐sided estimates of the Kolmogorov ‐diameters.

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“…The brand and price algorithm was applied to minimize the total number of containers used. The studies on the bin-packing problem that have been conducted previously addressed one or more constraints simultaneously, such as weight, priority of packing, orientation, hazardous goods, and multiple delivery points, in order to maximize the amount of cargo loaded into containers [24,25].…”

Section: Bin Packing Problemmentioning

confidence: 99%

Optimizing Container Fill Rates for the Textile and Garment Industry Using a 3D Bin Packing Approach

Thi Xuan Hoa

2024

HighTech. Innov. J.

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The scarcity of empty containers presents a significant logistical challenge globally. To address this issue, this study proposes the application of the optimal box arrangement in a container with a 3D bin packing problem to enhance fill rates and accommodate the complex packing criteria of the textile and garment industry. The study’s objective is to optimize box stacking into containers by considering various factors such as multiple product types, diverse box sizes, varying container sizes, and prioritizing stacking according to purchase orders (PO). In tackling the NP-hard problem with the added constraint of PO-based stacking, this study advocates employing a genetic algorithm combined with a wall-building algorithm to address practical challenges. The genetic algorithm demonstrates optimal efficacy in solving large-scale optimization problems within specified timeframes, yielding high-quality results. In addition, normalization methods are applied to convert box sizes to pallet sizes, expediting problem-solving and facilitating the selection of appropriate container sizes, namely 20- or 40-feet. The research findings indicate that the proposed method achieved a container fill rate of up to 91.67% and minimized the number of containers used. Doi: 10.28991/HIJ-2024-05-02-017 Full Text: PDF

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Conditions for the existence of a global strong solution to a class of nonlinear evolution equations in a Hilbert space

Cited by 7 publications

References 2 publications

Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type

Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type

The maximal regularity of the third‐order differential equation and its applications

Optimizing Container Fill Rates for the Textile and Garment Industry Using a 3D Bin Packing Approach

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