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[CT051]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Here, we present a mathematical model of a parabolic partial differential equation in a time-dependent domain for a phase change process. This non-linear problem includes moving phase change material and a size-dependent thermal conductivity. A numerical solution of the problem is proposed by using finite difference scheme. We also present the consistency, stability and convergency of the scheme for the considered problem. For a particular case, we propose the comparison of our result with the exact solution to show the accuracy of the proposed numerical solution, and it is observed that our calculated results are sufficiently closed to the exact results. The effects of various parameters on the phase change process are also discussed.
Classification : 35R37, 58J35, 80A22
Author(s) :
- Rajeev . (Indian Institute of Technology BHU Varanasi India )

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, we discuss a finite volume scheme for the three-dimensional barotropic compressible Euler equations driven by a multiplicative Brownian noise. We derive necessary a priori estimates for numerical approximations, and show that the Young measure generated by the numerical approximations converge to a dissipative measure-valued martingale solution to the stochastic compressible Euler system. These solutions are probabilistically weak in the sense that the driving noise and associated filtration are integral part of the solution. To the best of our knowledge, this is the first attempt to prove the convergence of numerical approximations for the underlying system.
Classification : 35R60, 76N10, 65N08
Author(s) :
- Ujjwal Koley (Associate Professor)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
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
Author(s) :
- Karthikeyan Shanmugasundaram (Periyar University)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We review recent developments in applications of convex integration to PDEs forced by various types of random noise. The examples of equations include the Navier-Stokes equations, Euler equations, Boussinesq system, MHD system, surface quasi-geostrophic equtaions, and power-law models. The types of noise include additive, linear multiplicative, trasport, nonlinear, space-time white noise, etc.
Classification : 35R60, 35A02, 76W05
Author(s) :
- Kazuo Yamazaki (Texas Tech University)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
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
Author(s) :
- Anguraj Annamalai (PSG College of Arts & Science, Coimbatore, Tamil Nadu, India)