Juncheng Wei's Books

Mathematical Aspects of Pattern Formation in Biological Systems

By: Juncheng Wei,Matthias Winter

Write a review Read reviews Take a Quiz Solve Book Puzzle

Mathematical Aspects of Pattern Formation in Biological Systems

By: Juncheng Wei,Matthias Winter

This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models. The approach adopted in the monograph is based on the following paradigms: • Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones • Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions • Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems. Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

324

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447155262

ISBN 13

9781447155263

On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System

By: Weiwei Ao,Chang-Shou Lin,Juncheng Wei

Write a review Read reviews Take a Quiz Solve Book Puzzle

On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System

By: Weiwei Ao,Chang-Shou Lin,Juncheng Wei

Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

100

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470415437

ISBN 13

9781470415433

The Lin-Ni's Problem for Mean Convex Domains

By: Olivier Druet,Frédéric Robert,Juncheng Wei

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Lin-Ni's Problem for Mean Convex Domains

By: Olivier Druet,Frédéric Robert,Juncheng Wei

The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.

Average ratings

N/A