Well-Posedness of History/State-Dependent Implicit Sweeping Processes

Zeng, Shengda; Vilches, Emilio

doi:10.1007/s10957-020-01730-w

Cited by 21 publications

(8 citation statements)

References 30 publications

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“…For all these reasons, various authors have developed of theory and applications for history-dependent operators to variational and hemivariational inequalities. For instance, see [20,23,[27][28][29][30][31]41] and the references therein. Besides, some recently important contributions on the topic of variational and hemivariational inequalities with applications to mixed boundary problems have been provided in [2,18,21,[37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Error bounds for a class of history-dependent variational inequalities controlled by $\mathcal{D}$-gap~functions

CHEN

Tâm

2023

Hacettepe Journal of Mathematics and Statistics

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In the present paper, we are concerned with investigating error bounds for history-dependent variational inequalities controlled by the difference gap (for brevity, D-gap) functions. First, we recall a class of elliptic variational inequalities involving the history-dependent operators (for brevity, HDVI). Then, we introduce a new concept of gap functions to the HDVI and propose the regularized gap function for the HDVI via the optimality condition for the concerning minimization problem. Consequently, the D-gap function for the HDVI depends on these regularized gap functions is established. Finally, error bounds for the HDVI controlled by the regularized gap function and the D-gap function are derived under suitable conditions.

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Section: Introductionmentioning

confidence: 99%

Error bounds for a class of history-dependent variational inequalities controlled by $\mathcal{D}$-gap~functions

CHEN

Tâm

2023

Hacettepe Journal of Mathematics and Statistics

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“…which is called the time-space fcGL equation with Kerr law nonlinearity [22]. Studying the solutions of nonlinear evolution equations has always been a very meaningful thing [31,32,39]. In 2018, Sulaiman obtained combined dark-bright and combined singular optical solitons of equation (1.1) by using the extended sinh-Gordon equation expansion method [36].…”

Section: Introductionmentioning

confidence: 99%

Wave solutions of the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity

Zhou

Cai

LİU>

2023

Hacettepe Journal of Mathematics and Statistics

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In this paper, the bifurcation theory of dynamical system is applied to investigate the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity. We mainly consider the case of α ≠ 2β which is not discussed in previous work. By overcoming some difficulties aroused by the singular traveling wave system, such as bifurcation analysis of nonanalytic vector field, tracking orbits near the full degenerate equilibrium and calculation of complicated elliptic integrals, we give a total of 20 explicit exact traveling wave solutions of the time-space fractional complex Ginzburg-Landau equation and classify them into 11 categories. Some new traveling wave solutions of this equation are obtained including the compactons and the bounded solutions corresponding to some bounded manifolds.

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“…Although the theory and computational techniques, optimal control problem for variational and hemivariational inequalities have been studied for quite some time now, it seems that there are still many unanswered questions and many interesting ideas are to be discovered. see, for example, Patrone (1977), Peng and Kunisch (2018), Shi (1988), Sofonea (2019), Zhou et al (2006), Zeng et al (2021), Zeng and Vilches (2020), , Liu et al (2019). Recently, Hung (2021) introduced a class of the controlled systems of fuzzy mixed quasi-hemivariational inequalities of the Minty type.…”

Section: Introductionmentioning

confidence: 99%

Painlevé–Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with application to controlling traffic networks under uncertainty

Hùng

Keller

2021

Comp. Appl. Math.

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The purpose of this article is to establish some new results on the Painlevé-Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with a sequence of mappings Γ C -converging. First, we introduce a new class of controlled systems for fuzzy vector quasi-optimization problems and establish some conditions for the existence of approximate solutions to these problems using the Kakutani-Fan-Glicksberg fixed-point theorem. Then, we study the Painlevé-Kuratowski lower convergence, Painlevé-Kuratowski upper convergence and Painlevé-Kuratowski convergence of the solution sets for such problems. Finally, as a real-world application, we consider the special case of controlled systems of fuzzy traffic network problems. Existence conditions and the Painlevé-Kuratowski convergence of the solution sets for these problems are also investigated and studied. The results presented in the paper are new and extend the main results given by some authors in the literature.

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Well-Posedness of History/State-Dependent Implicit Sweeping Processes

Cited by 21 publications

References 30 publications

Error bounds for a class of history-dependent variational inequalities controlled by $\mathcal{D}$-gap~functions

Error bounds for a class of history-dependent variational inequalities controlled by $\mathcal{D}$-gap~functions

Wave solutions of the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity

Painlevé–Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with application to controlling traffic networks under uncertainty

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