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[CT042]

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We study the exact internal and boundary controllability for a second order linear evolution problem defined in a two-component domain. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. The results are achieved via a constructive method known as Hilbert Uniqueness Method, HUM for short, introduced by J. -L. Lions. Unlike classical cases, we find lower bounds for the control times depending not only on the geometry of the domain and on the coefficient matrix of our problems but also on the coefficient of proportionality of the jump with respect to the conormal derivatives. References [1] S. Monsurro`, A. K. Nandakumaran, C. Perugia, Exact Internal Con- trollability for a Problem with Imperfect Interface, Appl. Math. Op- tim. (2022), 1-33. [2] S. Monsurro`, A. K. Nandakumaran, C. Perugia, A Note on the Exact Boundary Controllability for an Imperfect Transmission Problem, Ric. Mat. 40 (2021), 1-18.
Classification : 35LXX, 35QXX
Author(s) :
- Sara Monsurrò (University of Salerno)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : Motivated by the interplay of multiple species in several real world transport processes, we propose a bidirectional totally asymmetric simple exclusion process with two finite reservoirs regulating the inflow of oppositely directed particles corresponding to two different species. The system’s stationary characteristics such as densities, currents, etc., are investigated using a theoretical framework based on mean-field approximation and are supported by extensive Monte Carlo simulations. The impact of species, quantified by filling factor, has been comprehensively analyzed.
Classification : 35Lxx, 70Exx, 70Lxx, 37Axx
Author(s) :
- Ankita Gupta (Indian Institute of Technology Ropar)
- Bipasha Pal (Stockholm University)
- Arvind Kumar Gupta (Indian Institute of Technology Ropar)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : The work investigates the dynamical behavior of modified May-Holling-Tanner model in the presence of dynamic alternative resources. We study the role of dynamic alternative resources on the survival of the species when there is prey rarity. A detailed mathematical analysis and numerical evaluation have been presented to discuss the coexistence of species, stability, occurrence of different bifurcations in both the cases; in presence of prey and in absence of prey.
Classification : 37G15
Author(s) :
- Anuraj Singh (ABV-Indian Institute of Information Technology and Management Gwalior)
- Deepak Tripathi (ABV-Indian Institute of Information Technology and Management Gwalior)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We propose a delayed differential Equation model for HIV infection. We assume that the HIV infection process is not instantaneous, but instead, it is a delayed process due to delayed activation of immune response and drug action on HIV. The analysis of the model shows that the dynamics of interaction can be very much complex, and there can be various rich dynamics in this process. We analyze the model for possible bifurcation through some MATLAB numerical toolbox.
Classification : 37G15, 34K18
Author(s) :
- Saroj Kumar Sahani (South Asian University)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : Algebraic Riccati equations (AREs) have been extensively applied in linear optimal control problems and many efficient numerical methods were developed. The stabilizing (or almost stabilizing) solution has attracted the most attention among all Hermitian solutions of the ARE in the past works. Nevertheless, it is an interesting and challenging issue in finding the extremal solutions of AREs which play an important role in the applications. The contribution of this paper is twofold. Firstly, the existence of these extremal solutions is established under the framework of fixed-point iteration. Secondly, an accelerated fixed-point iteration (AFPI) based on the semigroup property is developed for computing four extremal solutions of the discrete-time algebraic Riccati equation. In addition, we prove that the convergence of the AFPI is at least R-suplinear with order $r>1$ under some mild assumptions. Numerical examples are shown to illustrate the feasibility and accuracy of the proposed algorithm.
Classification : 39B12, 39B42, 65H05, 15A24
Author(s) :
- Chun-Yueh Chiang (Center for General Education, National Formosa University)
- Hung-Yuan Fan (National Taiwan Normal University )