Read more
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms.
Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut
ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
List of contents
Introduction.- Linear Wave functions.- Sobolev inequality with Decay.- Estimates for solutions for linear wave equation.- Estimates for composition Function.
About the author
Many children dream of becoming dancers, musicians, actors, and artists, but few have the opportunity, the skill, and the determination to live out those dreams. Rachel Isadora is the exception. When she was young, she wanted to be a ballerina--and she became one. And now she has firmly established herself in a second career as an artist with an impressive string of picture books, including Ben's Trumpet, a Caldecott Honor Book.
Born and raised in New York City, Rachel studied at the School of American Ballet (associated with the New York City Ballet) as a Ford Foundation scholarship student. She danced with the Boston Ballet until a foot injury forced her to consider another career: book illustration. "I had always drawn for my own entertainment," says Rachel, "but I'd never had any instruction, and I wasn't sure how to proceed. So I just took a collection of sketches-odds and ends on bits of paper-to the first editor who would see me. She suggested I do a book about what I knew best." The result was Max, published in 1976 and named an ALA Notable Book.
Since Max, Rachel has written and illustrated many other books, and has illustrated three books by her editor, Elizabeth Shub. When Rachel begins a new book, she first imagines the story through the pictures. I 'see' each illustration separately," she says. "I write a description of what I envision on each page; then I go over it with my editor and make revisions. Next I do the actual drawing, and finally I write the text."
Rachel Isadora lives in New York City with her two children. When she is not busy with her family, she spends most of her spare time drawing. "Work like this is a dancer's fantasy," she says. "Because ballet is so demanding, dancers' stage careers are short. They can only dream of going on and on forever. With art, I can go on and on, and for me it's the only work that compares in intensity and joy."
Many children dream of becoming dancers, musicians, actors, and artists, but few have the opportunity, the skill, and the determination to live out those dreams. Rachel Isadora is the exception. When she was young, she wanted to be a ballerina--and she became one. And now she has firmly established herself in a second career as an artist with an impressive string of picture books, including Ben's Trumpet, a Caldecott Honor Book.
Born and raised in New York City, Rachel studied at the School of American Ballet (associated with the New York City Ballet) as a Ford Foundation scholarship student. She danced with the Boston Ballet until a foot injury forced her to consider another career: book illustration. "I had always drawn for my own entertainment," says Rachel, "but I'd never had any instruction, and I wasn't sure how to proceed. So I just took a collection of sketches-odds and ends on bits of paper-to the first editor who would see me. She suggested I do a book about what I knew best." The result was Max, published in 1976 and named an ALA Notable Book.
Since Max, Rachel has written and illustrated many other books, and has illustrated three books by her editor, Elizabeth Shub. When Rachel begins a new book, she first imagines the story through the pictures. I 'see' each illustration separately," she says. "I write a description of what I envision on each page; then I go over it with my editor and make revisions. Next I do the actual drawing, and finally I write the text."
Rachel Isadora lives in New York City with her two children. When she is not busy with her family, she spends most of her spare time drawing. "Work like this is a dancer's fantasy," she says. "Because ballet is so demanding, dancers' stage careers are short. They can only dream of going on and on forever. With art, I can go on and on, and for me it's the only work that compares in intensity and joy."
Summary
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms.
Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut
ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
