Stationary Pattern of a Ratio-Dependent Food Chain Model with Diffusion

The main purpose of this erratum is to correct an error in the proof of Theorem 4.4 in [R. Peng, J. Shi, and M. Wang, SIAM J. Appl. Math., 67 (2007), pp. 1479-1503]

Pattern formation of a Schnakenberg-type plant root hair initiation model

This paper concentrates on the diversity of patterns in a quite general Schnakenberg-type model. We discuss existence and nonexistence of nonconstant positive steady state solutions as well as their bounds. By means of investigating Turing, steady state and Hopf bifurcations, pattern formation, including Turing patterns, nonconstant spatial patterns or time periodic orbits, is shown. Also, the global dynamics analysis is carried out

Pattern formation of a Schnakenberg-type plant root hair initiation model

This paper concentrates on the diversity of patterns in a quite general Schnakenberg-type model. We discuss existence and nonexistence of nonconstant positive steady state solutions as well as their bounds. By means of investigating Turing, steady state and Hopf bifurcations, pattern formation, including Turing patterns, nonconstant spatial patterns or time periodic orbits, is shown. Also, the global dynamics analysis is carried out

Study on the set of stationary solutions for the Gray-Scott model

制度:新 ; 文部省報告番号:甲2503号 ; 学位の種類:博士(理学) ; 授与年月日:2007/10/25 ; 早大学位記番号:新462

A nonlocal Gray-Scott model: well-posedness and diffusive limit

Well-posedness in $L_\infty$ of the nonlocal Gray-Scott model is studied for integrable kernels, along with the stability of the semi-trivial spatially homogeneous steady state. In addition, it is shown that the solutions to the nonlocal Gray-Scott system converge to those to the classical Gray-Scott system in the diffusive limit

Traveling water waves — the ebb and flow of two centuries

This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical studies of periodic waves with critical layers that may overhang; existence, nonexistence, and qualitative theory of solitary waves and fronts; traveling waves with localized vorticity or density stratification; and waves in three dimensions

Proceedings of Seminar on Partial Differential Equations in Osaka 2012 : in honor of Professor Hiroki Tanabe’s 80th birthday

Osaka University, August 20‐24, 2012Edited by Atsushi Yagi and Yoshitaka Yamamot

Tropical cyclone intensification from finite amplitude disturbances, or, How hurricanes hardly happen.

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1991.Includes bibliographical references (p. 241-261).Sc.D

Bifurcation analysis of the Topp model

In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

2009 program of studies : nonlinear waves

The fiftieth year of the program was dedicated to Nonlinear Waves, a topic with many applications in geophysical fluid dynamics. The principal lectures were given jointly by Roger Grimshaw and Harvey Segur and between them they covered material drawn from fundamental theory, fluid experiments, asymptotics, and reaching all the way to detailed applications. These lectures set the scene for the rest of the summer, with subsequent daily lectures by staff and visitors on a wide range of topics in GFD. It was a challenge for the fellows and lecturers to provide a consistent set of lecture notes for such a wide-ranging lecture course, but not least due to the valiant efforts of Pascale Garaud, who coordinated the write-up and proof-read all the notes, we are very pleased with the final outcome contained in these pages. This year’s group of eleven international GFD fellows was as diverse as one could get in terms of gender, origin, and race, but all were unified in their desire to apply their fundamental knowledge of fluid dynamics to challenging problems in the real world. Their projects covered a huge range of physical topics and at the end of the summer each student presented his or her work in a one-hour lecture. As always, these projects are the heart of the research and education aspects of our summer study.Funding was provided by the National Science Foundation through Grant No. OCE-0824636 and the Office of Naval Research under Contract No. N00014-09-10844