Nonlinear theory of pseudodifferential equations on a halfline [EBook] / Nakao Hayashi and Elena Kaikina.
Nonlinear theory of pseudodifferential equations on a halfline [EBook] / Nakao Hayashi and Elena Kaikina.
This book is the first attempt to develop systematically a general theory of the initialboundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a halfline or on a segment. We study traditionally important problems, such as local and global existence of sol...
Personal Name(s):  Hayashi, Nakao. 

Kaikina, Elena.  
Edition: 
1st ed. 
Imprint: 
Amsterdam ; Boston :
Elsevier,
2004

Physical Description: 
1 online resource (xix, 340 p.) 
Note: 
englisch 
ISBN: 
0444515690 9780444515698 
Series Title: 
North Holland mathematics studies,
194 
Subject (LOC):  
Full Text 
This book is the first attempt to develop systematically a general theory of the initialboundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a halfline or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initialboundary value problems with a general pseudodifferential operator has not been well developed due to its difficulty. There are many open natural questions. Firstly how many boundary data should we pose on the initialboundary value problems for its correct solvability? As far as we know there are few results in the case of nonlinear nonlocal equations. The methods developed in this book are applicable to a wide class of dispersive and dissipative nonlinear equations, both local and nonlocal. For the first time the definition of pseudodifferential operator on a halfline and a segment is done A wide class of nonlinear nonlocal and local equations is considered Developed theory is general and applicable to different equations The book is written clearly, many examples are considered Asymptotic formulas can be used for numerical computations by engineers and physicists The authors are recognized experts in the nonlinear wave phenomena. 