# Registered Data

Contents

- 1 [CT030]
- 1.1 [00144] The flux perturbed Riemann solution for isentropic Cargo-LeRoux model
- 1.2 [02107] Nonlinear stochastic heat equation with variable thermal conductivity
- 1.3 [02659] Extension of p-Laplace type operator for image enhancement
- 1.4 [01755] A Study of Imaging in the Existence of Resonance with Multiple Scattering

# [CT030]

## [00144] The flux perturbed Riemann solution for isentropic Cargo-LeRoux model

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: In this research, we study the pressureless Cargo-LeRoux model of conservation laws, which is modeled from the one-dimensional constant gravity Euler equations. Introducing flux perturbation of a van der Waals isentropic gas equation of state, the exact solution of Riemann problem is derived and establish the existence and uniqueness of the Riemann solution globally. Finally, the influence of van der Waals excluded volume on the physical quantities is illustrated graphically using MATLAB software.**Classification**:__35D30__,__35L65__,__76L05__,__76N10__,__76N15__**Author(s)**:**Sahadeb Kuila**(DEPARTMENT OF MATHEMATICS, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu 603203)- Sumita Jana (DEPARTMENT OF MATHEMATICS, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu 603203)

## [02107] Nonlinear stochastic heat equation with variable thermal conductivity

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We consider a stochastic heat equation with variable thermal conductivity, on infinite domain, with both deterministic and stochastic source and with stochastic initial data. The stochastic source appears in the form of multiplicative generalized stochastic process. In our solving procedure we use regularized derivatives and the theory of generalized uniformly continuous semigroups of operators. We establish and prove the result concerning the existence and uniqueness of solution within certain generalized function space.**Classification**:__35D30__,__35K05__,__47D99__**Author(s)**:**Danijela Rajter-Ciric**(Faculty of Sciences, University of Novi Sad)- Milos Japundzic (Novi Sad School of Business - Higher Education Institution for Applied Studies)

## [02659] Extension of p-Laplace type operator for image enhancement

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: This talk is devoted to the study of operator $\Delta_{\{ \tau, \chi\}}u =|\nabla u|^{\tau(|\nabla u|)-1}(\Delta_1u + \chi(|\nabla u|)\Delta_{\infty}u) $, where $ \tau(s), \chi(s)\ge 0$. We establish the well-posedness of the Neumann boundary value problem for the parabolic equation $ u_t =\Delta_{\{\tau, \chi\}}u $ in the framework of viscosity solutions. Numerical simulations shows that this novel operator $\Delta_{\{ \tau, \chi\}}$ is superior both to the Perona-Malik and the total variation methods applied to image enhancement.**Classification**:__35D40__,__65M06__**Author(s)**:**Yuanji Cheng**(Malmo University)

## [01755] A Study of Imaging in the Existence of Resonance with Multiple Scattering

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: A random medium consisting of many small bodies that can reflect or scatter the incoming waves is called multiple scattering. Imaging becomes difficult to perform in such random media because of sharp responses arising from the underlying interactions of multiply scattered waves at resonance frequencies. In this talk, we present a study by simulating this problem with the Foldy-Lax-Lippmann-Schwinger formalism, which was employed for the multiply scattered waves, in randomly distributed isotropic point-like scatterers.**Classification**:__35P05__,__47B06__,__78A46__**Author(s)**:**Ray-Hon Sun**(Stanford University)- Ray-Hon Sun (Stanford University)