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Author: Yihong Du Publisher: World Scientific ISBN: 9812834737 Category : Mathematics Languages : en Pages : 373
Book Description
This book consists of survey and research articles expanding on the theme of the ?International Conference on Reaction-Diffusion Systems and Viscosity Solutions?, held at Providence University, Taiwan, during January 3?6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Waseda), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (Minnesota), Kunimochi Sakamoto (Hiroshima), Richard Tsai (Texas), Mingxin Wang (China), Yoshio Yamada (Waseda), Eiji Yanagida (Tohoku), and Xiao-Qiang Zhao (Canada).
Author: Yihong Du Publisher: World Scientific ISBN: 9812834737 Category : Mathematics Languages : en Pages : 373
Book Description
This book consists of survey and research articles expanding on the theme of the ?International Conference on Reaction-Diffusion Systems and Viscosity Solutions?, held at Providence University, Taiwan, during January 3?6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Waseda), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (Minnesota), Kunimochi Sakamoto (Hiroshima), Richard Tsai (Texas), Mingxin Wang (China), Yoshio Yamada (Waseda), Eiji Yanagida (Tohoku), and Xiao-Qiang Zhao (Canada).
Author: Antonin Chambolle Publisher: Springer Science & Business Media ISBN: 8876424733 Category : Mathematics Languages : en Pages : 276
Book Description
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
Author: Serena Dipierro Publisher: Springer ISBN: 303018921X Category : Mathematics Languages : en Pages : 502
Book Description
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Author: Nicholas D. Alikakos Publisher: Springer ISBN: 3319905724 Category : Mathematics Languages : en Pages : 349
Book Description
This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes – non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was settled in a series of papers: Ghoussoub and Gui (2d), Ambrosio and Cabré (3d), Savin (up to 8d), and del Pino, Kowalczyk and Wei (counterexample for 9d and above). This book extends, in various ways, the Caffarelli-Córdoba density estimates that played a major role in Savin's proof. It also introduces an alternative method for obtaining pointwise estimates. Key features and topics of this self-contained, systematic exposition include: • Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions. • Preliminary material beginning with the stress-energy tensor, via which monotonicity formulas, and Hamiltonian and Pohozaev identities are developed, including a self-contained exposition of the existence of standing and traveling waves. • Tools that allow the derivation of general properties of minimizers, without any assumptions of symmetry, such as a maximum principle or density and pointwise estimates. • Application of the general tools to equivariant solutions rendering exponential estimates, rigidity theorems and stratification results. This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations – ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or the applied mathematics of materials science.
Author: Philippe Bénilan Publisher: Longman Scientific and Technical ISBN: Category : Mathematics Languages : en Pages : 374
Book Description
This volume collects most of the lectures and communications presented to the International Conference which took place in Nancy in March 1988. The main issues addressed were: nonlinear elliptic equations and systems, parabolic equations, time-dependent systems and the calculus of variations.
Author: Maurizio Falcone Publisher: World Scientific ISBN: 9789812799807 Category : Mathematics Languages : en Pages : 256
Book Description
Geometrical optics and viscosity solutions / A.-P. Blanc, G. T. Kossioris and G. N. Makrakis -- Computation of vorticity evolution for a cylindrical Type-II superconductor subject to parallel and transverse applied magnetic fields / A. Briggs ... [et al.] -- A characterization of the value function for a class of degenerate control problems / F. Camilli -- Some microstructures in three dimensions / M. Chipot and V. Lecuyer -- Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow / K. Deckelnick and G. Dziuk -- Optimal discretization steps in semi-lagrangian approximation of first-order PDEs / M. Falcone, R. Ferretti and T. Manfroni -- Convergence past singularities to the forced mean curvature flow for a modified reaction-diffusion approach / F. Fierro -- The viscosity-duality solutions approach to geometric pptics for the Helmholtz equation / L. Gosse and F. James -- Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations / L. Grune -- Solution and application of anisotropic curvature driven evolution of curves (and surfaces) / K. Mikula -- An adaptive scheme on unstructured grids for the shape-from-shading problem / M. Sagona and A. Seghini -- On a posteriori error estimation for constant obstacle problems / A. Veeser.
Author: Yihong Du
Author: Yihong Du
Author: Panayotis G. Kevrekidis
Author: Antonin Chambolle
Author: Serena Dipierro
Author: Nicholas D. Alikakos
Author: Philippe Bénilan
Author: 
Author: 
Author: Maurizio Falcone
Author: American Mathematical Society