Emerging topics on differential equations and their applications : proceedings on Sino-Japan Conference of Young Mathematicians on Emerging Topics on Differential Equations and their Applications, Nankai University, China, 5-9 December 2011 / / edited by Hua Chen, Yiming Long, Yasumasa Nishiura

• Pubblicazione: Singapore, : World Scientific Pub. Co., 2013
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (319 p.)
• Disciplina: 515.353
• Soggetto topico: Differential equations
• Altri autori: ChenHua LongYiming NishiuraYasumasa
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Preface; CONTENTS; A Spectral Theory of Linear Operators on Rigged Hilbert Spaces under Certain Analyticity Conditions H. Chiba; 1. Introduction; 2. A review of the spectral theory on rigged Hilbert spaces; References; Conditional Fredholm Determinant and Trace Formula for Hamiltonian Systems: a Survey X.-J. Hu and P.-H. Wang; 1. Introduction; 2. Hill Formula for S-periodic Hamiltonian systems; 2.1. Trace finite condition and conditional Fredholm determinant; 2.2. Hill formula and its application; 3. Trace formula in Hamiltonian systems; Acknowledgement; References ; Initial Value Problem for Water Waves and Shallow Water and Long Wave Approximations T. Iguchi 1. Introduction; 2. Initial Value Problem; 3. Shallow Water Approximations; 3.1. Shallow water equations; 3.2. Tsunami generation; 3.3. Green-Naghdi equations; 4. Long Wave Approximations; 4.1. KdV equation; 4.2. Kawahara equation; 4.3. Forced KdV equation; 4.4. Benjamin-Ono equation; References; On the Existence and Nonexistence of Maximizers Associated with Trudinger-Moser Type Inequalities in Unbounded Domains M. Ishiwata; 1. Introduction and main results; 2. Proof of Theorem 1.1 ; 3. Proof of Theorem 1.24. Proof of Theorem 1.3; References; Computer-assisted Uniqueness Proof for Stokes' Wave of Extreme Form K. Kobayashi; 1. Introduction; 2. The idea behind the proof of uniqueness; 3. Numerical results; 4. Conclusion; Funding; Acknowledgements; References; From the Boltzmann H-theorem to Perelman's W-entropy formula for the Ricci flow X.-D. Li; 1. Introduction; 2. History and Boltzmann entropy formula; 2.1. Thermodynamic entropy; 2.2. Boltzmann equation and H-theorem; 2.3. Boltzmann entropy formula; 2.4. Shannon and Nash entropy ; 2.5. The maximum entropy principle and the central limit theorem 2.6. Canonical ensemble and Boltzmann's entropy formula; 3. Perelman's interpretation of the W-entropy for Ricci flow; 4. A probabilistic interpretation of the W-entropy for Ricci flow; 5. Comparison between Boltzmann's H-theorem and Perelman's entropy formula; 6. An open problem: the "density of states" measure for the Ricci flow; Acknowledgement; References; The Spreading of a New Species with Free Boundaries X. Liu and B. Lou; 1. Introduction; 2. Convergence Results; 2.1. Dichotomy and trichotomy; 2.2. Key lemmas of the proof ; 3. Asymptotic spreading speed References; Recent Progress on Observability for Stochastic Partial Differential Equations Q. Lu and Z.-Q. Yin; 1. Introduction; 2. Observability estimate for stochastic parabolic equation; 3. Observability estimate for stochastic hyperbolic equations; 4. Observability estimate for stochastic Schrodinger equations; 5. Some open problems; Acknowledgement; References; The Nonlinear "Hot Spots" Conjecture in Balls of S2 and H2 Y. Miyamoto; 1. Introduction and Main results; 2. Preliminaries; 3. Proofs; 3.1. Proofs of Theorems 1.1 (i) and 1.2 (i) ; 3.2. Proofs of Theorems 1.1 (ii) and 1.2 (ii)
• Sommario/riassunto: The aim of the Sino-Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems.
• Titolo autorizzato: Emerging topics on differential equations and their applications
• ISBN: 1-299-46279-0; 981-4449-75-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910815368803321
• Lo trovi qui: Univ. Federico II
• Serie: Nankai series in pure, applied mathematics and theoretical phyics ; ; v. 10.