scholarly journals Existence and stability of one-peak symmetric stationary solutions for the Schnakenberg model with heterogeneity

2019 ◽  
Vol 39 (5) ◽  
pp. 2807-2875 ◽  
Author(s):  
Yuta Ishii ◽  
◽  
Kazuhiro Kurata
Keyword(s):  
Stationary Solutions ◽  
Schnakenberg Model ◽  
Existence And Stability

Existence and stability of static shells for the Vlasov–Poisson system

Analysis ◽  
2006 ◽  
Vol 26 (4) ◽  
Author(s):  
Achim Schulze
Keyword(s):  
Spherical Symmetry ◽  
Variational Approach ◽  
Stationary Solutions ◽  
Poisson System ◽  
Existence And Stability

We prove the existence and stability of stationary solutions to the Vlasov–Poisson System with spherical symmetry, which describe static shells, i.e., the support of their densities is bounded away from the origin. We use a variational approach which was established by Y. Guo and G. Rein.

scholarly journals Existence and stability of static shells for the Vlasov–Poisson system with a fixed central point mass

2009 ◽  
Vol 146 (2) ◽  
pp. 489-511
Author(s):  
ACHIM SCHULZE
Keyword(s):  
Black Hole ◽  
Simple Model ◽  
Variational Approach ◽  
Existence Result ◽  
Stationary Solutions ◽  
Point Mass ◽  
Classical Solutions ◽  
Poisson System ◽  
Existence And Stability ◽  
Global Existence Result

AbstractWe consider the Vlasov–Poisson system with spherical symmetry and an exterior potential which is induced by a point mass in the center. This system can be used as a simple model for a newtonian galaxy surrounding a black hole. For this system, we establish a global existence result for classical solutions with shell-like initial data, i.e. the support of the density is bounded away from the point mass singularity. We also prove existence and stability of stationary solutions which describe static shells, where we use a variational approach which was established by Y. Guo and G. Rein.

Numerical approach to existence and stability of stationary solutions to a SKT cross-diffusion equation

2018 ◽  
Vol 28 (11) ◽  
pp. 2191-2210 ◽  
Author(s):  
Tatsuki Mori ◽  
Takashi Suzuki ◽  
Shoji Yotsutani
Keyword(s):  
Diffusion Equation ◽  
Numerical Investigation ◽  
Numerical Approach ◽  
Stationary Solutions ◽  
Spatial Segregation ◽  
Population Pressure ◽  
Cross Diffusion ◽  
Habitat Area ◽  
Representation Of Solutions ◽  
Existence And Stability

The SKT cross-diffusion equation is proposed by N. Shigesada, K. Kawasaki and E. Teramoto in 1979 to investigate segregation phenomena of two competing species with each other in the same habitat area. The effect of cross-diffusion affects the population pressure between two different species. Lou and Ni derived limiting systems to see whether this effect may give rise to a spatial segregation or not, and to clarify its mechanism. In this paper, we introduce some new representation of solutions to a stationary limiting problem modified from representation by Lou, Ni and Yotsutani. We apply it to the numerical investigation of existence, non-existence, multiplicity and stability.

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