Partial Differential Equations: Classification, Properties and Applications


Deborah E. Richards (Editor)

Series: Mathematics Research Developments
BISAC: MAT007000

This book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. The authors also investigate nonlinear control problems for couple partial differential equations arising from climate and circulation dynamics in the equatorial zone; the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras; and the existence and properties of solutions, applications in sequential optimal control with pointwise in time state constraints.
(Imprint: Nova)



Table of Contents


The Lax-Milgram Theorem and Some Applications to Partial Differential Equation
(Paul Bracken, Department of Mathematics, University of Texas, Edinburg, TX, USA)

Coupled PDEs and Control Systems Arising in Climate Dynamics: Ocean-Atmosphere Interactions and Tropical Instability Waves
(Aziz Belmiloudi, Institut de Recherche MAthématique de Rennes (IRMAR), Rennes, France)

Integration of PDE with the help of Analysis over Octonions and Cayley-Dickson Algebras
(Sergey V. Ludkovsky, Department of Applied Mathematics, Moscow State Technical University MIREA, Moscow, Russia)

Mixed Boundary-Value Problem for Divergent Hyperbolic PDE: Existence and Properties of Solutions, Applications in Sequential Optimal Control with Pointwise in Time State Constraints
(Vladimir S. Gavrilov and Mikhail I. Sumin, Mechanics and Mathematics Faculty, Nizhnii Novgorod State University, Nizhnii Novgorod, Russia)


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