Registered Data
Contents
- 1 [CT036]
- 1.1 [00010] Convergence Analysis of Fourth Order Extended Fisher Kolmogorov Equation Using Quintic Hermite Splines
- 1.2 [00519] Non-Newtonian fluids with discontinuous-in-time stress tensor.
- 1.3 [00820] Chemotaxis system with signal-dependent motility and the singular limit problem
- 1.4 [00487] A strongly nonlinear anisotropic parabolic-elliptic system: analysis and numerical simulation
- 1.5 [00735] Turing instability of a diffusive predator-prey model with Monod-Haldane response
[CT036]
[00010] Convergence Analysis of Fourth Order Extended Fisher Kolmogorov Equation Using Quintic Hermite Splines
- 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)
[00519] Non-Newtonian fluids with discontinuous-in-time stress tensor.
- 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)
[00820] Chemotaxis system with signal-dependent motility and the singular limit problem
- 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)
[00487] A strongly nonlinear anisotropic parabolic-elliptic system: analysis and numerical simulation
- 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)
[00735] Turing instability of a diffusive predator-prey model with Monod-Haldane response
- 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 )