Keywords:
Differential equations, partial.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (114 pages)
Edition:
1st ed.
ISBN:
9789811028427
Series Statement:
SpringerBriefs in Mathematics Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=4737166
DDC:
515.35
Language:
English
Note:
Intro -- Preface -- Contents -- 1 First Order Quasilinear Hyperbolic Systems -- 1.1 1-D First Order Quasilinear Hyperbolic Systems -- 1.2 Characteristic Form of Hyperbolic System -- 1.3 Reducible Quasilinear Hyperbolic System. Riemann Invariants -- 1.4 Saint-Venant System for Unsteady Flows on a Single Open Canal -- 1.5 Semi-global C1 Solutions to the Mixed Initial-Boundary Value Problem -- 1.6 Exchanging the Role of t and x -- 1.7 Uniqueness of C1 Solution to the One-Sided Mixed Initial-Boundary Value Problem -- 2 Quasilinear Wave Equations -- 2.1 1-D Quasilinear Wave Equations -- 2.2 Semi-global C2 Solutions to the Mixed Initial-Boundary Value Problem -- 2.3 Uniqueness of C2 Solution to the One-Sided Mixed Initial-Boundary Value Problem -- 3 Semi-global Piecewise Classical Solutions on a Tree-Like Network -- 3.1 Introduction -- 3.2 Semi-global Piecewise C1 Solutions to 1-D First Order Quasilinear Hyperbolic Systems on a Tree-Like Network -- 3.3 Semi-global Piecewise C2 Solutions to 1-D Quasilinear Wave Equations on a Tree-Like Network -- 4 Exact Boundary Controllability of Nodal Profile for 1-D First Order Quasilinear Hyperbolic Systems -- 4.1 Introduction -- 4.2 Definitions and Main Results -- 4.3 Proof of Theorem 4.1 -- 4.4 Proof of Theorem 4.2 -- 4.5 Exact Boundary Controllability of Nodal Profile for Saint-Venant System -- 4.6 Remarks -- 5 Exact Boundary Controllability of Nodal Profile for 1-D First Order Quasilinear Hyperbolic Systems on a Tree-Like Network -- 5.1 Exact Boundary Controllability of Nodal Profile for Saint-Venant System on a Star-Like Network of Open Canals (Case 1) -- 5.2 Exact Boundary Controllability of Nodal Profile for Saint-Venant System on a Star-Like Network of Open Canals (Case 2).
,
5.3 Exact Boundary Controllability of Nodal Profile for Saint-Venant System on a Star-Like Network of Open Canals (Case 3) -- 5.4 Exact Boundary Controllability of Nodal Profile for Saint-Venant System on a Star-Like Network of Open Canals (Case 4) -- 5.5 Exact Boundary Controllability of Nodal Profile for Saint-Venant System on a Star-Like Network of Open Canals (Case 5) -- 5.6 Exact Boundary Controllability of Nodal Profile for Saint-Venant System on a Tree-Like Network of Open Canals -- 5.7 Exact Boundary Controllability of Nodal Profile for Saint-Venant System on a Tree-Like Network of Open Canals (Continued) -- 5.8 Remarks -- 6 Exact Boundary Controllability of Nodal Profile for 1-D Quasilinear Wave Equations -- 6.1 Introduction -- 6.2 Definitions and Main Results -- 6.3 Proof of Theorem 6.1 -- 6.4 Proof of Theorem 6.2 -- 6.5 Remarks -- 7 Exact Boundary Controllability of Nodal Profile for 1-D Quasilinear Wave Equations on a Planar Tree-Like Network of Strings -- 7.1 Introduction -- 7.2 Exact Boundary Controllability of Nodal Profile for 1-D Quasilinear Wave Equations on a Star-Like Network of Strings -- 7.3 Exact Boundary Controllability of Nodal Profile for 1-D Quasilinear Wave Equations on a Star-Like Network of Strings (Continued) -- 7.4 Exact Boundary Controllability of Nodal Profile for Quasilinear Wave Equations on a Planar Tree-Like Network of Strings -- 7.5 Exact Boundary Controllability of Nodal Profile for Quasilinear Wave Equations on a Planar Tree-Like Network (Continued) -- 7.6 Remarks -- References -- Index.
