Evolution Equations With A Complex Spatial Variable
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| Title: | Evolution Equations With A Complex Spatial Variable |
|---|---|
| Description: | 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 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. |
| Authors: | Ciprian G Gal, Sorin G Gal, Jerome A Goldstein |
| Resource Type: | eBook. |
| Subjects: | Evolution equations, Variables (Mathematics) |
| Categories: | MATHEMATICS / Differential Equations / Partial, MATHEMATICS / Applied, MATHEMATICS / Complex Analysis |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf – Type: ebook-epub Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Evolution Equations With A Complex Spatial Variable – Name: Abstract Label: Description Group: Ab Data: 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 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ciprian+G+Gal%22">Ciprian G Gal</searchLink><br /><searchLink fieldCode="AR" term="%22Sorin+G+Gal%22">Sorin G Gal</searchLink><br /><searchLink fieldCode="AR" term="%22Jerome+A+Goldstein%22">Jerome A Goldstein</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Evolution+equations%22">Evolution equations</searchLink><br /><searchLink fieldCode="DE" term="%22Variables+%28Mathematics%29%22">Variables (Mathematics)</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Differential+Equations+%2F+Partial%22">MATHEMATICS / Differential Equations / Partial</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Applied%22">MATHEMATICS / Applied</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Complex+Analysis%22">MATHEMATICS / Complex Analysis</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 515.353 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Evolution equations Type: general – SubjectFull: Variables (Mathematics) Type: general Titles: – TitleFull: Evolution Equations With A Complex Spatial Variable Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ciprian G Gal – PersonEntity: Name: NameFull: Sorin G Gal – PersonEntity: Name: NameFull: Jerome A Goldstein – PersonEntity: Name: NameFull: Ciprian G Gal – PersonEntity: Name: NameFull: Sorin G Gal – PersonEntity: Name: NameFull: Jerome A Goldstein IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2014 – D: 26 M: 04 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9789814590594 – Type: isbn-electronic Value: 9789814590600 – Type: isbn-electronic Value: 9789814590617 Numbering: – Type: volume Value: 00014 Titles: – TitleFull: Evolution Equations With A Complex Spatial Variable Type: main |
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