scholarly journals A new class of fractional impulsive differential hemivariational inequalities with an application

2022 ◽  
Vol 27 ◽  
pp. 1-22
Author(s):  
Yun-hua Weng ◽  
Tao Chen ◽  
Nan-jing Huang ◽  
Donal O'Regan
Keyword(s):  
Differential Equation ◽  
Impulsive Differential Equation ◽  
Convergence Result ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
New Class ◽  
Perturbation Problem ◽  
Perturbation Data ◽  
The Stability ◽  
Stability Of The Solution

We consider a new fractional impulsive differential hemivariational inequality, which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result, which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.

scholarly journals Differential variational–hemivariational inequalities: existence, uniqueness, stability, and convergence

2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Guo-ji Tang ◽  
Jinxia Cen ◽  
Van Thien Nguyen ◽  
Shengda Zeng
Keyword(s):  
Nonlinear Evolution Equation ◽  
Original Problem ◽  
Nonlinear Evolution ◽  
Convergence Result ◽  
Hemivariational Inequality ◽  
Stability And Convergence ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Kkm Principle ◽  
Stability Of The Solution

AbstractThe goal of this paper is to study a comprehensive system called differential variational–hemivariational inequality which is composed of a nonlinear evolution equation and a time-dependent variational–hemivariational inequality in Banach spaces. Under the general functional framework, a generalized existence theorem for differential variational–hemivariational inequality is established by employing KKM principle, Minty’s technique, theory of multivalued analysis, the properties of Clarke’s subgradient. Furthermore, we explore a well-posedness result for the system, including the existence, uniqueness, and stability of the solution in mild sense. Finally, using penalty methods to the inequality, we consider a penalized problem-associated differential variational–hemivariational inequality, and examine the convergence result that the solution to the original problem can be approached, as a parameter converges to zero, by the solution of the penalized problem.

scholarly journals Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Furi Guo ◽  
Jinrong Wang ◽  
Jiangfeng Han
Keyword(s):  
Differential Equation ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Impulsive Differential Equation ◽  
Frictional Contact ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Pseudomonotone Operator ◽  
Weak Formulation ◽  
Uniqueness Results

<p style='text-indent:20px;'>This paper deals with a class of history-dependent frictional contact problem with the surface traction affected by the impulsive differential equation. The weak formulation of the contact problem is a history-dependent hemivariational inequality with the impulsive differential equation. By virtue of the surjectivity of multivalued pseudomonotone operator theorem and the Rothe method, existence and uniqueness results on the abstract impulsive differential hemivariational inequalities is established. In addition, we consider the stability of the solution to impulsive differential hemivariational inequalities in relation to perturbation data. Finally, the existence and uniqueness of weak solution to the contact problem is proved by means of abstract results.</p>

scholarly journals Partial differential hemivariational inequalities

2018 ◽  
Vol 7 (4) ◽  
pp. 571-586 ◽  
Author(s):  
Zhenhai Liu ◽  
Shengda Zeng ◽  
Dumitru Motreanu
Keyword(s):  
Evolution Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Upper Semicontinuity ◽  
Solution Set ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Well Posedness ◽  
Partial Differential ◽  
New Class

AbstractThe aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution equations and hemivariational inequalities. First, we introduce the concept of strong well-posedness for mixed variational quasi hemivariational inequalities and establish metric characterizations for it. Then we show the existence of solutions and meaningful properties such as measurability and upper semicontinuity for the solution set of the mixed variational quasi hemivariational inequality associated to the partial differential hemivariational inequality. Relying, on these properties we are able to prove the existence of mild solutions for partial differential hemivariational inequalities. Furthermore, we show the compactness of the set of the corresponding mild trajectories.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Marine Exopolysaccharide Complexed With Scandium Aimed as Theranostic Agents

Molecules ◽  
2021 ◽  
Vol 26 (4) ◽  
pp. 1143 ◽  
Author(s):  
Mattia Mazza ◽  
Cyrille Alliot ◽  
Corinne Sinquin ◽  
Sylvia Colliec-Jouault ◽  
Pascal E. Reiller ◽  
...  
Keyword(s):  
Nuclear Medicine ◽  
Light Scattering ◽  
Molar Mass ◽  
Field Flow Fractionation ◽  
High Concentration ◽  
New Class ◽  
Free Ion ◽  
Theranostic Agents ◽  
The Stability ◽  
Drug Reference

(1) Background: Exopolysaccharide (EPS) derivatives, produced by Alteromonas infernus bacterium, showed anti-metastatic properties. They may represent a new class of ligands to be combined with theranostic radionuclides, such as 47Sc/44Sc. The goal of this work was to investigate the feasibility of such coupling. (2) Methods: EPSs, as well as heparin used as a drug reference, were characterized in terms of molar mass and dispersity using Asymmetrical Flow Field-Flow Fractionation coupled to Multi-Angle Light Scattering (AF4-MALS). The intrinsic viscosity of EPSs at different ionic strengths were measured in order to establish the conformation. To determine the stability constants of Sc with EPS and heparin, a Free-ion selective radiotracer extraction (FISRE) method has been used. (3) Results: AF4-MALS showed that radical depolymerization produces monodisperse EPSs, suitable for therapeutic use. EPS conformation exhibited a lower hydrodynamic volume for the highest ionic strengths. The resulting random-coiled conformation could affect the complexation with metal for high concentration. The LogK of Sc-EPS complexes have been determined and showing that they are comparable to the Sc-Hep. (4) Conclusions: EPSs are very promising to be coupled with the theranostic pair of scandium for Nuclear Medicine.

scholarly journals Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integral Form ◽  
Collocation Methods ◽  
Nonlinear Odes ◽  
New Class ◽  
New Methods ◽  
Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

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