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[CT026]

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : The asymptotic behavior of solutions as a small parameter tends to zero is determined for a variety of singular-limit PDEs. In some cases even existence for a time independent of the small parameter was not known previously. New examples for which uniform existence does not hold are also presented. Some of the results are joint work with Samuel Nordmann.
Classification : 35B25, 35B40
Author(s) :
- Steve Schochet (Tel Aviv University)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We provide characterizations of diffusion matrices A for which the sequence of solutions $(u^{\varepsilon})_{\varepsilon > 0}$ to $-A(x/\varepsilon):D^2 u^{\varepsilon} = f$ in $\Omega$, $u^{\varepsilon} = g$ on $\partial\Omega$, converges to the solution of the homogenized problem with $L^{\infty}$-rate $\mathcal{O}(\varepsilon^2)$ for all sufficiently regular $f,g$. Whereas such diffusion matrices can be characterized via the third-order homogenized tensor, we provide more explicit characterizations and prove an open conjecture posed by Guo and Tran.
Classification : 35B27, 35B40, 35J25
Author(s) :
- Xiaoqin Guo (University of Cincinnati)
- Timo Sprekeler (National University of Singapore)
- Hung Vinh Tran (University of Wisconsin Madison)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We discus extension to Orlicz spaces of two scale convergence method in homogenization and apllication. Reiterated two scale convergence method and unfolding method is also presented in those Space which generilize standard Sobolev spaces and capture more information. We apply Above method on a number of problem including nonlinear degenerated elliptic operator with nonstandart growth.
Classification : 35B27, 35B40, 35J25, 35J60, 35J70
Author(s) :
- Joel Fotso Tachago (The University of Bamenda)
- Joel Fotso Tachago (The University of Bamenda)
- Hubert Nnang (University of Yaoundé 1)
- Elvira Zappale (University of Roma 1)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We present a multi-phase model to study the reduction of quartz to silicon carbide in a laboratory-scale reactor. We model the transport of gases and solids, and the kinetics of the reactions involved in the reduction process. Through the analysis of the model, we aim to gain a better understanding of the underlying mechanisms driving the reduction of quartz and to identify key parameters that can be controlled to optimize the production of silicon carbide.
Classification : 35B30, 35E15, 35Q49, 35R37
Author(s) :
- Brady Metherall (University of Oxford)

Session Date & Time : 3E (Aug.23, 17:40-19:20)
Type : Contributed Talk
Abstract : We consider a nonlinear SIS epidemic model with nonlocal disease transmission rate and diffusion in space which is a system of parabolic equations. The existence and uniqueness of steady state are studied using compact and nonsupporting operators, and strongly continuous semigroup theory, respectively. Due to the nonlinearity in the disease transmission rate, proof of the uniqueness of a steady state requires a completely different approach. The linearization around the nontrivial steady state of the model requires the study of a perturbed operator. Spectral analysis is used to study the local stability and the global stability of the steady state.
Classification : 35B35, 35Q92, 47H10, 92D25
Author(s) :
- Soumak Nag (University of Hyderabad)
- Suman Kumar Tumuluri (University of Hyderabad)