Evolution equations with a complex spatial variable:
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, Schrodinger and Korteweg–de Vries equations. The complexification of the spatial variable is done...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific Pub. Co.
c2014
|
| Series: | Series on concrete and applicable mathematics
v. 14 |
| Subjects: | |
| Online Access: | FHN01 Volltext |
| 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, Schrodinger 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 preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought. For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane |
| Physical Description: | x, 191 p |
| ISBN: | 9789814590600 |
Staff View
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| 520 | |a 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, Schrodinger 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 preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought. For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane | ||
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| id | DE-604.BV044640349 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:57Z |
| institution | BVB |
| isbn | 9789814590600 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030038322 |
| oclc_num | 1012713611 |
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| physical | x, 191 p |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| series2 | Series on concrete and applicable mathematics |
| spelling | Gal, Ciprian G. 1977- Verfasser aut Evolution equations with a complex spatial variable Ciprian G. Gal, Sorin G. Gal, Jerome A. Goldstein Singapore World Scientific Pub. Co. c2014 x, 191 p txt rdacontent c rdamedia cr rdacarrier Series on concrete and applicable mathematics v. 14 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, Schrodinger 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 preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought. For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane Evolution equations Variables (Mathematics) Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s 1\p DE-604 Gal, Sorin G. Sonstige oth Goldstein, Jerome A. 1941- Sonstige oth Erscheint auch als Druck-Ausgabe 9789814590594 http://www.worldscientific.com/worldscibooks/10.1142/9113#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gal, Ciprian G. 1977- Evolution equations with a complex spatial variable Evolution equations Variables (Mathematics) Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4129061-6 |
| title | Evolution equations with a complex spatial variable |
| title_auth | Evolution equations with a complex spatial variable |
| title_exact_search | Evolution equations with a complex spatial variable |
| title_full | Evolution equations with a complex spatial variable Ciprian G. Gal, Sorin G. Gal, Jerome A. Goldstein |
| title_fullStr | Evolution equations with a complex spatial variable Ciprian G. Gal, Sorin G. Gal, Jerome A. Goldstein |
| title_full_unstemmed | Evolution equations with a complex spatial variable Ciprian G. Gal, Sorin G. Gal, Jerome A. Goldstein |
| title_short | Evolution equations with a complex spatial variable |
| title_sort | evolution equations with a complex spatial variable |
| topic | Evolution equations Variables (Mathematics) Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Evolution equations Variables (Mathematics) Evolutionsgleichung |
| url | http://www.worldscientific.com/worldscibooks/10.1142/9113#t=toc |
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