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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Evolution Equations With A Complex Spatial Variable (Hardcover)
Loot Price: R2,096
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Evolution Equations With A Complex Spatial Variable (Hardcover)
Series: Series on Concrete & Applicable Mathematics, 14
Expected to ship within 18 - 22 working days
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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, Schroedinger 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.
General
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