Registered Data

[CT025]

[00692] Well-posedness with large data for a weighted porous medium equation

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : The large data problem for the porous medium equation is to determine the optimal class of initial data for which local well-posedness is guaranteed for the Cauchy problem. The starting point is the classical results by Widder for the heat equation $u_t=\Delta u$ and later those of Benilan, Crandall, and Pierre for the porous medium equation $u_t=\Delta u^m$ for $m>1$. We extend these results for weighted equations $\rho(x)u_t=\Delta u^m$ for $\rho(x)\cong|x|^{-\gamma}$ for $\gamma\in(0,2)$.
  • Classification : 35A01, 35A02, 35B45, 35K55
  • Author(s) :
    • Troy Petitt (Politecnico di Milano)
    • Matteo Muratori (Politecnico di Milano)

[01069] Global existence and stability of three species predator-prey system with prey-taxis

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : In this paper, we study the initial-boundary value problem of a three species predator-prey system with prey-taxis which describes the indirect prey interactions through a shared predator in a bounded domain $\Omega \subset \mathbb{R}^n (n\geq 1)$with smooth boundary and homogeneous Neumann boundary conditions. The model parameters are assumed to be positive constants. We first prove the global existence of classical solutions under suitable assumptions on the prey-taxis coefficients $\chi_1,\chi_2$ and $d$. Moreover, we establish the global stability of the prey-only state and coexistence steady states by using Lyapunov functionals and LaSalle's invariance principle.
  • Classification : 35A01, 35B35, Partial differential equations and Mathematical Biology ( To prove Global existence and stability for chemotaxis systems and predator-prey systems )
  • Author(s) :
    • GURUSAMY ARUMUGAM (The Hong Kong Polytechnic University )

[02641] Reconstructing electron backscatter diffraction data using vectorized total variation flow

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : Polycrystalline materials consist of crystal grains with distinct grain orientations and crystal structure. Electron backscatter diffraction is used to record the grain orientation. This orientation data might contain noise as well as the missing regions. We propose reconstructing the orientation data using weighted total variation flow, which is a pde obtained from solving the minimization problem. We then fill the missing region using the TV flow. This talk discusses the application of this reconstruction technique.
  • Classification : 35A15
  • Author(s) :
    • Emmanuel Atoleya Atindama (Clarkson University)
    • Prashant Athavale (Clarkson University)
    • Gunay Dogan (National Institute of Standards and Technology)

[02026] Variants of the penalty method for contact problems - Formulations unifying Nitsche and penalty methods

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : The penalty method is a simple yet effective computational technique of handling unilateral contact problems. In addition to its inconsistent, this method is often criticized of ill-conditioning when the penalty parameter goes to zero. We propose here new penalty methods overcoming the conditioning issue. We also established that some of our penalty formulations are equivalent of variants of Nitsche’s method, meaning that the inconsistent of these penalty methods is insignificant.
  • Classification : 35A35, 65J15, 74M15, 74B05
  • Author(s) :
    • Ibrahima Dione (Professor at Moncton university)

[02662] ASYMMETRICAL CELL DIVISION WITH EXPONENTIAL GROWTH

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : An advanced pantograph-type partial differential equation, supplemented with initial and boundary conditions, arises in a model of asymmetric cell division. Methods for solving such problems are limited owing to functional (nonlocal) terms. The separation of variables entails an eigenvalue problem that involves a nonlocal ordinary differential equation. We discuss plausible eigenvalues that may yield nontrivial solutions to the problem for certain choices of growth and division rates of cells. We also consider the asymmetric division of cells with linear growth rate which corresponds to “exponential growth” and exponential rate of cell division, and show that the solution to the problem is a certain Dirichlet series. The distribution of the first moment of the biomass is shown to be unimodal.
  • Classification : 35F10, 35R10
  • Author(s) :
    • Ali Ashher Zaidi (LUMS, Lahore)
    • Bruce van-Brunt (Massey University New Zealand)
    • Muhammad Mohsin (LUMS, Lahore)