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[CT039]

[00073] Scattering behavior for one dimensional wave maps into Riemannian manifolds

  • Session Date & Time : 2E (Aug.22, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : In this talk, we explore the scattering behavior for wave maps from Minkowski space $\mathbb{R}^{1+1}$ into general Riemannian manifolds, provided the initial data are small. In particular, we show that the nonlinear scattering operator can be linearized as the corresponding linear scattering operator. The underlying physical intuition of this conclusion is that one-dimensional wave maps behave exactly in the same manner as their scattering fields detected by the far-away observers.
  • Classification : 35L05, 35A01, 35B40, 35P25, 35R30
  • Author(s) :
    • Mengni Li (Southeast University)

[02609] Reliable and efficient a posteriori error estimates for time-dependent wave equations

  • Session Date & Time : 2E (Aug.22, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : I will discuss a novel equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. Specifically, I will show that the estimator provides fully-guaranteed upper bounds that are asymptotically constant-free and that it is efficient and polynomial-degree-robust, meaning that the efficiency constant does not deteriorate as the approximation order is increased. To the best of my knowledge, this work is the first to propose an estimator for the wave equation that is provably reliable and efficient in the same norm. I will present numerical examples illustrate the theory and suggest that it is sharp.
  • Classification : 35L05, 65M15, 65M20, 65M60
  • Author(s) :
    • Théophile Chaumont-Frelet (Inria)

[00275] A fast data-driven method for designing compressible shock dominant flows

  • Session Date & Time : 2E (Aug.22, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : We will present a new class of high-order numerical algorithms for computational fluid dynamics. Called "GP-MOOD," the new finite volume method is based on the Gaussian Processes modeling that generalizes the Gaussian probability distribution. Solutions at shocks and discontinuities are handled by the improved Multidimensional Optimal Order Detection (MOOD) strategy, which controls numerical stability and accuracy in an "a posteriori" shock-capturing formalism. We also introduce a new data-driven "a priori" MOOD method.
  • Classification : 35L25, 76N15, 85-08, 65M08
  • Author(s) :
    • Dongwook Lee (University of California Santa Cruz)

[00079] Multi-dimensional Optimal Systems for Chaplygin Gas Cargo-LeRoux model

  • Session Date & Time : 2E (Aug.22, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : The famous Cargo-LeRoux model for the isentropic Chaplygin gas is studied using classical Lie symmetry method. Optimal systems up to six-dimensions are constructed using the adjoint transformation and the invariants of the admitted Lie algebras. We obtain exact solutions to the Cargo-LeRoux model by using the one-dimensional optimal system and discussed the physical behavior of the solutions graphically. Finally, We discussed the evolutionary behavior of a discontinuity wave.
  • Classification : 35L40, 70G65, 76N15
  • Author(s) :
    • Manoj Kumar Pandey (BITS Pilani K K Birla Goa Campus)
    • Pabitra Kumar Pradhan (BITS Pilani K K Birla Goa Campus)

[00159] Wave interactions in drift- flux equations of two-phase flows

  • Session Date & Time : 2E (Aug.22, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : In this talk, we consider the interactions of arbitrary shocks for a $3\times 3$ system of conservation laws governing drift-flux equations of two-phase flows with isothermal and isentropic equation of states. Here, we use the properties of Riemann solution and interaction of weak shocks for this study. Consequently, we reduce the system of equations by taking the projection of shocks in the phase plane to investigate the interactions of arbitrary shocks.
  • Classification : 35L40, 35L45, 35L65, 35L67, Hyperbolic system of conservation laws
  • Author(s) :
    • Minhajul Minhajul (Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, India)
    • Rakib Mondal (Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, India)