# Registered Data

Contents

- 1 [CT036]
- 1.1 [00820] Chemotaxis system with signal-dependent motility and the singular limit problem
- 1.2 [00634] Bifurcation curves for semipositone problem with Minkowski-curvature operator
- 1.3 [00519] Non-Newtonian fluids with discontinuous-in-time stress tensor.
- 1.4 [00010] Convergence Analysis of Fourth Order Extended Fisher Kolmogorov Equation Using Quintic Hermite Splines

# [CT036]

**Session Time & Room****Classification**

## [00820] Chemotaxis system with signal-dependent motility and the singular limit problem

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G502__**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__**Format**: Talk at Waseda University**Author(s)**:**Changwook Yoon**(Chungnam National University)- Yong-Jung Kim (KAIST)

## [00634] Bifurcation curves for semipositone problem with Minkowski-curvature operator

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G502__**Type**: Contributed Talk**Abstract**: We study the shape of bifurcation curve of positive solutions for the semipositone Minkowski-curvature problem $-\left( u^{\prime }/\sqrt{1-{u^{\prime }}^{2}}\right) ^{\prime }=\lambda f(u),$ in $\left( -L,L\right) $, and $u(-L)=u(L)=0,$ where $\lambda ,L>0$ and $\left( \beta -u\right) f(u)<0$ for $u>0$. We prove that if $f$ is either convex or concave, then the bifurcation curve is C-shaped.**Classification**:__34B15__,__34B18__,__34C23__,__74G35__**Format**: Talk at Waseda University**Author(s)**:**Shao-Yuan Huang**(National Taipei University of Education)

## [00519] Non-Newtonian fluids with discontinuous-in-time stress tensor.

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G502__**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__**Format**: Talk at Waseda University**Author(s)**:- Miroslav Bulicek (Charles University)
- Piotr Gwiazda (Polish Academy of Sciences)
- Jakub Skrzeczkowski (University of Warsaw)
**Jakub Woźnicki**(University of Warsaw)

## [00010] Convergence Analysis of Fourth Order Extended Fisher Kolmogorov Equation Using Quintic Hermite Splines

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G502__**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__**Format**: Online Talk on Zoom**Author(s)**:**Shelly Arora**(Punjabi University, Patiala)- Priyanka Bhardwaj (Punjabi University, Patiala)
- Saroj Kumar Sahani (South Asian University, New Delhi)