On the Ulam stability and existence of $ L^p $-solutions for fractional differential and integro-differential equations with Caputo-Hadamard derivative by Abduljawad Anwar, Shayma Adil Murad

“…The paper delves into preliminary results, the existence and uniqueness of $ L^p $ solutions to the boundary value problem, and presents the Ulam-Hyers stability. …”
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An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers by Vasyl Chekurin, Yurij Boychuk

“…A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. …”
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Investigation of heat and mass transfer of free convective MHD flow along a vertical plate in a porous medium using the new modified differential transform-decomposition method by Helena Nayar, Patrick Azere Phiri

“…The method is found to be applicable directly to the boundary value problem, and successful in producing analytic solutions.…”
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Singular Solutions to a (3 + 1)-D Protter-Morawetz Problem for Keldysh-Type Equations by Nedyu Popivanov, Tsvetan Hristov, Aleksey Nikolov, Manfred Schneider

“…We study a boundary value problem for (3 + 1)-D weakly hyperbolic equations of Keldysh type (problem PK). …”
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RESEARCH CONCAVE CIRCULAR HOLE TEMPLATE LINEAR VARIABLE THICKNESS STIFFNESS AND STRENGTH THEORIES by LI ShaoJie

“…This paper studies linear variable thickness circular aperture concave template theory of stiffness and strength calculation.First,set up mechanical model:Template for circular concave,outside the perimeter fixed; center has a round hole,inside the perimeter free,outside under uniformly distributed vertical load.Secondly,the establishment of mathematical model:Derivation of concave template in the axisymmetric condition,ordinary differential equation with variable coefficients of elastic curved surface,and gives the mathematical expressions of boundary conditions.Again,in view of the differential equation boundary value problem,the displacement method and the Matlab algorithm,it is concluded that the deflection of concave template function,and establish the stiffness calculation condition of concave template.Then,determine the concave template on the bending moment and the maximum bending moment and stress,so as to establish a concave template strength calculation conditions.Finally,numerical examples.This paper presents the function solutions,to change law of control concave template section variable parameters.In this way,not only highlight the interdependent relationship between the quantity of each,and optimization,and discussion and application.The result is suitable for uniform,continuous,isotropic material artifacts.Because in the process of calculation and data processing with error,so the formula is similar.…”
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Elastic crack-tip stress field in a semi-strip by Victor Reut, Natalya Vaysfeld, Zinaida Zhuravlova

“…The one-dimensional problem is formulated as the vector boundary value problem which is solved with the help of matrix differential calculations and Green�s matrix apparatus. …”
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A strain based Lipschitz regularization for materials undergoing damage by Kamasamudram, Vasudevan, Stainier, Laurent

“…Data Driven Computational Mechanics (DDCM) solves the boundary value problem by directly relying on the strain-stress data, bypassing the need for a constitutive model. …”
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Fracture processes numerical modeling of elastic-brittle bodies with statistically distributed subregions strength values by Eugeniia Feklistova, Artur Mugatarov, Valeriy Wildemann, Anton Agishev

“…The novel formulation of the boundary value problem and its solution algorithm are developed. …”
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Seepage consolidation during elastic body deformation under normal load by F.M. Kadyrov, A.V. Kosterin, E.V. Skvortsov

“…It has been shown that the sum of effective normal stresses satisfies the heat equation and can be found as a solution to the corresponding boundary value problem. A pressure-related auxiliary function that satisfies the Laplace equation has been introduced. …”
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Implementation of a practical sand constitutive model coupled with the high cycle accumulation framework in PLAXIS by Pishun Tantivangphaisal, David M.G. Taborda, Stavroula Kontoe

“…A reference 15 MW offshore wind turbine monopile foundation subject to lateral cyclic wave loading is used in an engineering design scenario at three different load levels to verify the current numerical implementation.Details include: • Modifications made to the HCA framework to couple it with a practical sand constitutive model, • Implementation of an efficient workflow to switch between low and high cycle constitutive equations in PLAXIS, and • Verification of the implementation at single element and boundary value problem scales.…”
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Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow by Cui-Cui Sheng, Jin-Zhou Zhao, Yong-Ming Li, Shun-Chu Li, Hu Jia

“…The SCMS is a straightforward method for differential equation's boundary value problems with complex boundary conditions, especially for solving the reservoir models in petroleum engineering.…”
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Crack path predictions and experiments in plane structures considering anisotropic properties and material interfaces by P.O. Judt, A. Ricoeur

“…Numerical crack paths are predicted based on FE calculations of the boundary value problem in connection with an intelligent adaptive re-meshing algorithm. …”
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Elastic crack-tip stress field in a semi-strip by Victor Reut, Natalya Vaysfeld, Zinaida Zhuravlova

“…The one-dimensional problem is formulated as the vector boundary value problem which is solved with the help of matrix differential calculations and Green’s matrix apparatus. …”
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Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales by Yanning Wang, Jianwen Zhou, Yongkun Li

“…Then, as an application, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a p-Laplacian conformable fractional differential equation boundary value problem on time scale T:  Tα(Tαup-2Tα(u))(t)=∇F(σ(t),u(σ(t))), Δ-a.e.  …”
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On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations by Peter I. Kogut, Olha P. Kupenko, Rosanna Manzo

“…We deal with the control object when we cannot expect to have a solution of the corresponding boundary value problem in the standard functional space for all admissible controls. …”
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Qualitative Properties of the Solution of a Conjugate Problem of Thermal Convection by A. A. Azanov, E. N. Lemeshkova

“…The inverse initial-boundary value problem describes convection near the temperature extremum point on the lower solid wall in a two-layer system. …”
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Modeling the hydrodynamics of the OWC device placed over an undulated seabed in the presence of ocean current by Santanu Kumar Dash, Kshma Trivedi, Santanu Koley, Shrabani Mondal

“…The boundary element method is used to address the corresponding boundary value problem. A significant attention is devoted to the analysis of the effectiveness and horizontal wave force exerted on the frontal barrier of the oscillating water column device by considering various values of incident wave and current parameters, as well as structural parameters related to both the oscillating water column device and the undulated seabed. …”
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A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid by Le Thi Phuong Ngoc, Truong Thi Nhan, Nguyen Thanh Long

“…We study the following initial-boundary value problem {ut − μt+αt(∂/∂t)∂2u/∂x2+(γ/x)(∂u/∂x) + fu = f1x,t, 1<x<R, t>0; u(1,t)=g1(t), u(R,t)=gR(t); u(x,0)=u~0(x)}, where γ>0,R>1 are given constants and f,f1,g1,gR,u~0,α, and μ are given functions. …”
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On optimization of substrate removal in a bioreactor with wall attached and suspended bacteria by Alma Mašić, Hermann J. Eberl

“…In the two-objective optimal control problem, the flow rate between the vessels is selected as the control variable.The treatment reactor is modelled by a system of three ordinary differential equations in which a two-point boundary value problem is embedded. The solution of the associated singular optimal control problem in the class of measurable functions is impractical to determine and infeasible to implement in real reactors. …”
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Numerical Estimation of Effective Mechanical Properties for Reinforced Plexiglas in the Two-Dimensional Case by Vladimir Levin, Ignatiy Vdovichenko, Anatoly Vershinin, Maksim Yakovlev, Konstantin Zingerman

“…The algorithm is based on consecutive application of different boundary conditions to representative surface elements (RSEs) in terms of displacements, solution of elastic boundary value problem for each case, and averaging the stress field obtained. …”
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