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[CT030]

CT030 (1/1) : Generalized solutions to partial differential equations (35D) / Parabolic equations and parabolic systems (35K) / Spectral theory and eigenvalue problems for partial differential equations (35P)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
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
Format : Talk at Waseda University
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)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
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
Format : Talk at Waseda University
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)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
Type : Contributed Talk
Abstract : We study the existence of a capacity solution to a nonlinear coupled parabolic-elliptic system. This system is a generalization of the so-called thermistor problem which models a temperature dependent electrical resistor. In this analysis we have considered the case where $Au$ is an operator of the Leray-Lions class defined in an anisotropic Sobolev space. We also show some numerical simulations of this problem and we discuss the obtained results.
Classification : 35K55, 35J70, 46E35
Format : Talk at Waseda University
Author(s) :
- Francisco Ortegón Gallego (Universidad de Cádiz)
- Manar Lahrache (Moulay Ismail University)
- Mohamed Rhoudaf (Moulay Ismail University)
- Hajar Talbi (Moulay Ismail University)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @G502
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)