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# [CT019]

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

## [00018] Structures and evolution of bifurcation diagrams for a one-dimensional diffusive generalized logistic problem with constant yield harvesting

**Session Time & Room**:__5B__(Aug.25, 10:40-12:20) @__G401__**Type**: Contributed Talk**Abstract**: We study the diffusive generalized logistic problem with constant yield harvesting: \begin{equation*} \left \{ \begin{array}{ll} u^{\prime \prime }(x)+\lambda g(u)-\mu =0, & -10$. We prove that, for any fixed $\mu >0,$ on the $(\lambda ,\left \Vert u\right \Vert _{\infty })$-plane, the bifurcation diagram consists of a $\subset $-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying $\mu >0.$ **Classification**:__34B18__,__74G35__**Format**: Talk at Waseda University**Author(s)**:**Shin-Hwa Wang**(National Tsing Hua University, TAIWAN)- Kuo-Chih Hung (National Chin-Yi University of Technology, Taiwan)
- Yiu-Nam Suen (National Tsing Hua University, TAIWAN)

## [01883] An application to the generalized logistic growth model

**Session Time & Room**:__5B__(Aug.25, 10:40-12:20) @__G401__**Type**: Contributed Talk**Abstract**: We study the bifurcation curves for a Dirichlet problem with geometrically concave nonlinearity. We give an application to the generalized logistic growth model. There are totally six qualitatively bifurcation curves.**Classification**:__34B18__,__74G35__**Format**: Talk at Waseda University**Author(s)**:**Kuo-Chih Hung**(National Chin-Yi University of Technology)- Kuo-Chih Hung (National Chin-Yi University of Technology)

## [01163] An infinite class of shocks for compressible Euler

**Session Time & Room**:__5B__(Aug.25, 10:40-12:20) @__G401__**Type**: Contributed Talk**Abstract**: We consider the two dimensional compressible Euler equations with azimuthal symmetry and construct an infinite class of shocks by establishing shock formation for a new Hölder family of so-called pre-shocks for all nonnegative integers. Moreover, a precise description of the dominant Riemann variable in the Hölder space is given in the form of a fractional series expansion.**Classification**:__35L67__,__35Q31__,__76N15__,__76L05__**Format**: Talk at Waseda University**Author(s)**:**Calum Rickard**(University of California, Davis)- Sameer Iyer (University of California, Davis)
- Steve Shkoller (University of California, Davis)
- Vlad Vicol (New York University)