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[CT036]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : An improvised collocation technique has been proposed to discretize multi-parameter fourth order non-linear extended Fisher Kolmogorov equation. The spatial direction has been discretized with quintic Hermite splines whereas temporal direction has been discretized with weighted finite difference scheme. The fourth order equation in space direction has been decomposed into second order using space splitting by introducing a new variable. The space splitting has been proposed to improvise the convergence of approximate solution. The proposed equation has been analyzed on uniform grid in both space and time directions. Error bounds for general order Hermite splines are established. $\epsilon$- uniform rate of convergence for the proposed scheme has also been discussed elaborately. The technique is illustrated by various numerical examples and error growth has been discussed by computing $L_2$ and $L_\infty$ norms.
Classification : 35K41, 35K55, 65M70, 65N35
Author(s) :
- Shelly Arora (Punjabi University, Patiala)
- Priyanka Bhardwaj (Punjabi University, Patiala)
- Saroj Kumar Sahani (South Asian University, New Delhi)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We consider the system of equations describing the flow of incompressible fluids in bounded domain. Here, the Cauchy stress tensor has asymptotically $(s-1)$-growth with the parameter $s$ depending on the spatial and time variable. We do not assume any smoothness of $s$ with respect to time variable. Such a setting is a natural choice if the material properties are instantaneous. We establish the existence of weak solution provided that $s\ge\frac{3d+2}{d+2}$.
Classification : 35K51, 35Q30, 76D05
Author(s) :
- Miroslav Bulicek (Charles University)
- Piotr Gwiazda (Polish Academy of Sciences)
- Jakub Skrzeczkowski (University of Warsaw)
- Jakub Woźnicki (University of Warsaw)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We study the reaction-diffusion model that consists of equations that govern the evolution of bio-cells in a chemotactic environment. In our modeling framework, we assume that if the chemical concentration is low, then the cells move actively, whereas if the chemical concentration is high, they become less active. As we take a limit of conversion process, we formally obtain the singular limit problem of Fokker-Planck type diffusion. The aim of this study is to prove the global well-posedness of the singular limit problem and its convergence rigorously.
Classification : 35K51, 35K57, 92C17
Author(s) :
- Changwook Yoon (Chungnam National University)
- Yong-Jung Kim (KAIST)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
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
Author(s) :
- Francisco Ortegón Gallego (Universidad de Cádiz)
- Manar Lahrache (Moulay Ismail University)
- Mohamed Rhoudaf (Moulay Ismail University)
- Hajar Talbi (Moulay Ismail University)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, we discuss the asymptotic behavior and Hopf bifurcation of the Monod-Haldane predator-prey model with diffusion. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. The diffusion-driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally, we show the numerical simulations provided to illustrate theoretical results.
Classification : 35K57, 92B05, Reaction-diffusion equations
Author(s) :
- Muniyagounder Sambath (Periyar University )