Registered Data

[CT024]

  • Session Time & Room
    • CT024 (1/1) : 2E @G402 [Chair: Önder Türk]
  • Classification
    • CT024 (1/1) : Partial differential equations (35-) / Qualitative properties of solutions to partial differential equations (35B) / Dynamic equations on time scales or measure chains (34N) / Partial differential equations and systems of partial differential equations with constant coefficients (35E)

[02961] An analysis of boundary variations in Laplace-Steklov eigenvalue problems

  • Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
  • 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
  • Format : Talk at Waseda University
  • Author(s) :
    • Önder Türk (Middle East Technical University)
    • Eylem Bahadır (Gebze Technical University)

[00698] Rigidity for Sobolev inequalities and radial PDEs on Cartan-Hadamard manifolds

  • Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
  • Type : Contributed Talk
  • Abstract : We aim at classifying all the Cartan-Hadamard manifolds supporting an optimal function for the $p$-Sobolev inequality. We prove that, under the validity of the Cartan-Hadamard conjecture, which is known to be true in dimension $n\le 4$, the only such manifold is $\mathbb{R}^n$, up to isometries. We also investigate radial solutions to the related $p$-Laplace Lane-Emden equation, obtaining rigidity of finite-energy solutions regardless of optimality. Furthermore, we study the asymptotic behavior of infinite-energy solutions.
  • Classification : 35B53, 35J92, 58J05, 58J70, 46E35
  • Format : Talk at Waseda University
  • Author(s) :
    • Matteo Muratori (Politecnico di Milano)
    • Nicola Soave (Politecnico di Milano)

[02197] Mean-field diffusive coupling to promote dispersal, synchronisation and stability of infectious diseases

  • Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
  • 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
  • Format : Online Talk on Zoom
  • Author(s) :
    • Tina Verma (Thapar Instiute of Engineering & Technology)

[01139] Adaptive sampling and transfer learning techniques for solution of PDEs

  • Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
  • 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
  • Format : Online Talk on Zoom
  • Author(s) :
    • Andreas Aristotelous (The University of Akron)

[00009] Numerical Solution of Kuramoto–Sivashinsky Equation Using Orthogonal Collocation with Bessel Polynomials as Basis

  • Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
  • 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
  • Format : Online Talk on Zoom
  • Author(s) :
    • Shelly Arora (Punjabi University, Patiala)
    • Indu Bala (Punjabi University, Patiala)