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[CT051]

CT051 (1/1) : Miscellaneous topics in partial differential equations (35R) / General topics in partial differential equations (35A)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
Type : Contributed Talk
Abstract : In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations. Under suitable assumptions, the bounds of the explosion times are obtained by using explicit solutions of an associated system of random PDEs and a formula due to Yor. We provide an estimate for the probability of the finite-time blow-up and the impact of the noise on the solution is investigated.
Classification : 35R60, 60H15, 74H35
Format : Talk at Waseda University
Author(s) :
- Karthikeyan Shanmugasundaram (Periyar University)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
Type : Contributed Talk
Abstract : In this paper, we discuss the asymptotic behavior of mild solutions of nonlinear stochastic partial functional equations driven by Poisson jumps and the Rosenblatt process in a Hilbert space. The Rosenblatt process is the simplest non-Gaussian Hermite process. It has continuous non-differentiable paths and is self-similar with stationary increments. It is Murray Rosenblatt who first conceived of it. The results are obtained by using the Banach fixed point theorem and the theory of resolvent operator developed by Grimmer. Finally, an example is provided to illustrate the effectiveness of the obtained results.
Classification : 35R60, 60H15, Stochastic Differential Equations
Format : Talk at Waseda University
Author(s) :
- Anguraj Annamalai (PSG College of Arts & Science, Coimbatore, Tamil Nadu, India)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
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 )
Format : Talk at Waseda University
Author(s) :
- GURUSAMY ARUMUGAM (The Hong Kong Polytechnic University )

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
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
Format : Online Talk on Zoom
Author(s) :
- Ibrahima Dione (Professor at Moncton university)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G702
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)