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[CT024]

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : The scope of mediated infectious diseases is strongly impacted by mobility of humans and mediating agents. The movement of hosts and mediators determines how spatially contagious infectious diseases are spread. Therefore, the metapopulation dynamics of mediated infectious disease model is examined in a patchy scenario where the hosts' and mediators' populations are divided into subpopulations. The network of humans and mediators are utilized to depict the patchy environment. The network patches are connected by mean field diffusive coupling. The patches of related networks synchronize and achieve bistable states as a result of dispersal.
Classification : 34N05
Author(s) :
- Tina Verma (Thapar Instiute of Engineering & Technology)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : An adaptive sampling technique applied to the deep Galerkin method (DGM), and separately a transfer learning algorithm also applied to DGM is examined, aimed to improve, and speed up the training of the deep neural network when learning the solution of partial differential equations (PDEs). The proposed algorithms improve the DGM method. The adaptive sampling scheme implementation is natural and efficient. Tests applied to selected PDEs discussing the robustness of our methods are presented.
Classification : 35-04, 65-04, Deep learning for the solution of PDEs
Author(s) :
- Andreas Aristotelous (The University of Akron)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : We analyse a Poisson-Nernst-Planck-Fermi model to describe the evolution of a mixture of finite size ions in liquid electrolytes, which move through biological membranes or nanopores. The global-in-time existence of bounded weak solutions and the weak-strong uniqueness result are proved, via entropy and relative entropy, respectively. Furthermore, an implicit Euler finite-volume scheme for the model is analysed and some simulations are shown.
Classification : 35-XX, Mathematical and numerical analysis of cross-diffusion system via entropy and relative entropy
Author(s) :
- Annamaria Massimini (TU Wien)
- Ansgar Jüngel (TU Wien)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : We analyze the influence of boundary perturbations on the spectrum of Laplace-Steklov eigenvalue problems. Both the differential equation and a boundary condition involve the spectral parameter. We derive Hadamard type expressions for the variation of the eigenvalues as the problem domain deforms. Consequently, we provide the convergence characteristics of the eigenvalues on the perturbed domain as its boundary approaches to that of the unperturbed one. Numerical results are obtained using a finite element formulation.
Classification : 35-XX, 65-XX, FEM analysis of eigenvalues in PDEs
Author(s) :
- Önder Türk (Middle East Technical University)
- Eylem Bahadır (Gebze Technical University)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : Bessel polynomials has been proposed as a base function in orthogonal collocation to discretize fourth order Kuramoto-Sivashinsky equation. Convergence of numerical results have been analysed through L2 and L∞ norms to discuss the effectiveness of technique. Number of test problems have been solved and comparison of results in space as well as in time direction at different number of collocation points has been presented. The numerical values are presented graphically to confirm applicability of technique.
Classification : 35E15, 35G20, 65M70, 33C10
Author(s) :
- Shelly Arora (Punjabi University, Patiala)
- Indu Bala (Punjabi University, Patiala)