TY  - BOOK
AU  - Taira,Kazuaki
TI  - Analytic semigroups and semilinear initial boundary value problems
T2  - London Mathematical Society lecture note series
SN  - 9780511662362 (ebook)
AV  - QA377 .T27 1995
U1  - 515/.353 20
PY  - 1995///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Differential equations, Parabolic
KW  - Boundary value problems
KW  - Semigroups
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Ch. I. Theory of Analytic Semigroups -- Ch. II. Sobolev Imbedding Theorems -- Ch. III. L[superscript p] Theory of Pseudo-Differential Operators -- Ch. IV. L[superscript p] Approach to Elliptic Boundary Value Problems -- Ch. V. Proof of Theorem 1 -- Ch. VI. Proof of Theorem 2 -- Ch. VII. Proof of Theorems 3 and 4 -- Appendix: The Maximum Principle
N2  - This book provides a careful and accessible exposition of the function analytic approach to initial boundary value problems for semilinear parabolic differential equations. It focuses on the relationship between two interrelated subjects in analysis: analytic semigroups and initial boundary value problems. This semigroup approach can be traced back to the pioneering work of Fujita and Kato on the Navier-Stokes equation. The author studies non homogeneous boundary value problems for second order elliptic differential operators, in the framework of Sobolev spaces of Lp style, which include as particular cases the Dirichlet and Neumann problems, and proves that these boundary value problems provide an example of analytic semigroups in Lp. This book will be a necessary purchase for researchers with an interest in analytic semigroups or initial value problems
UR  - https://doi.org/10.1017/CBO9780511662362
ER  -