Evolution equations with a complex spatial variable / Ciprian G. Gal, Sorin G. Gal, Jerome A. Goldstein.

Format:

Book

Author/Creator:

Gal, Ciprian G., 1977- author.

Gal, Sorin G., author.

Goldstein, Jerome A., 1941- author.

Series:

Series on concrete and applicable mathematics ; Volume 14.

Series on concrete and applicable mathematics, 1793-1142 ; Volume 14

Language:

English

Subjects (All):

Evolution equations.

Variables (Mathematics).

Physical Description:

1 online resource (202 p.)

Place of Publication:

Singapore : World Scientific, 2014.

Language Note:

English

Summary:

This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black-Merton-Scholes, Schrödinger and Korteweg-de Vries equations. The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions p

Contents:

Preface; Contents; 1. Historical background and motivation; 1.1 Historical background on the heat equation; 1.2 Summary of main results; 1.3 Derivations and physical interpretations; 2. Heat and Laplace equations of complex spatial variables; 2.1 Introduction; 2.2 Heat-type equations; 2.3 Laplace-type equations; 2.4 Extensions to several complex spatial variables; 2.5 Notes; 3. Higher-order heat and Laplace equations with complex spatial variables; 3.1 Introduction; 3.2 Preliminary results; 3.3 Higher-order heat and Laplace equations; 3.4 Extensions to several complex spatial variables

3.5 Notes4. Wave and telegraph equations with complex spatial variables; 4.1 Introduction; 4.2 Wave-type equations; 4.3 Telegraph-type equations; 4.4 Extensions to several complex spatial variables; 4.5 Notes and open problem; 5. Burgers and Black-Merton-Scholes equations with complex spatial variables; 5.1 Introduction; 5.2 Burgers-type equations; 5.3 Black-Merton-Scholes equations; 6. Schrodinger-type equations with complex spatial variables; 6.1 Introduction; 6.2 Schrodinger equations; 6.3 Higher-order Schrodinger equations; 6.4 Extensions to several complex spatial variables; 6.5 Note

7. Linearized Korteweg-de Vries equations with complex spatial variables7.1 Introduction; 7.2 Linearized Korteweg-de Vries type equations; 7.3 Extensions to several complex spatial variables; 8. Evolution equations with a complex spatial variable ingeneral domains; 8.1 The Faber derivative; 8.2 Heat and Laplace equations; 8.3 Higher-order heat and Laplace equations; 8.4 Wave and telegraph equations; 8.5 Schrodinger equations; 8.6 Concrete examples; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

981-4590-60-6