Partial Differential Equations - Brossura

Friedman, Avner

Brossura

ISBN 10: 0486469190 ISBN 13: 9780486469195

Casa editrice: Dover Pubns, 2008

Riassunto

This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.
Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of weak derivatives, proves various inequalities and imbedding problems, and derives smoothness theorems. Part Two concerns evolution equations in Banach space and develops the theory of semigroups. It solves the initial-boundary value problem for parabolic equations and covers backward uniqueness, asymptotic behavior, and lower bounds at infinity. The final section includes independent topics directly related to the methods and results of the previous material, including the analyticity of solutions of elliptic and parabolic equations, asymptotic behavior of solutions of elliptic equations near infinity, and problems in the theory of control in Banach space.

Su questo libro

Contenuti

Part 1. Elliptic Equations 1. Definitions 2. Green's Identity 3. Fundamental Solutions 4. Construction of Fundamental Solutions 5. Partition of Unity 6. Weak and Strong Derivatives 7. Strong Derivative as a Local Property 8. Calculus Inequalities 9. Extended Sobolev Inequalities in R(superscript n) 10. Extended Sobolev Inequalities in Bounded Domains 11. Imbedding Theorems 12. Gärding's Inequality 13. The Dirichlet Problem 14. Existence Theory 15–16. Regularity in the Interior 17. Regularity on the Boundary 18. A Priori Inequalities 19. General Boundary Conditions 20. Problems Part 2. Evolution Equations 1. Strongly Continuous Semigroups 2. Analytic Semigroups 3. Fundamental Solutions and the Cauchy Problems 4–5. Construction of Fundamental Solutions 6. Uniqueness of Fundamental Solutions 7. Solution of the Cauchy Problem 8. Differentiability of Solutions 9. The Initial-Boundary Value Problem for Parabolic Equations 10. Smoothness of the Solutions of the Initial-Boundary Value Problem 11. A Differentiability Theorem in Hilbert Space 12. A Uniqueness Theorem in Hilbert Space 13. Convergence of Solutions as t --> infinity 14. Fractional Powers of Operators 15. Proof of Lemma 14.5 16. Nonlinear Evolution Equations 17. Nonlinear Parabolic Equations 18. Uniqueness for Backward Equations 19. Lower Bounds on Solutions as t --> infinity 20. Problems Part 3. Selected Topics 1. Analyticity of Solutions of Elliptic Equations 2. Analyticity of Solutions of Evolution Equations 3. Analyticity of Solutions of Parabolic Equations 4. Lower Bounds for Solutions of Evolution Inequalities 5. Weighted Elliptic Equations 6. Asymptotic Expansions of Solutions of Evolution Equations 7. Asymptotic Behavior of Solutions of Elliptic Equations 8. Integral Equations in Banach Space 9. Optimal Control in Banach Space Bibliographical Remarks Bibliography

Product Description

This three-part treatment focuses on elliptic and evolution equations. Largely self-contained, this volume concludes with a series of independent topics related to the methods and results of preceding sections and introduces advanced topics for further study. Geared toward graduate and postgraduate students, it also constitutes a valuable reference for professionals. 1969 edition.

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 0486469190
• ISBN 13: 9780486469195
• Rilegatura: Copertina flessibile
• Numero di pagine: 262
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia