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dc.contributor.authorPapanicolaou, Vassilis ( Orcid Icon 0000-0001-5405-7297 )
dc.contributor.authorKallitsi, Eva ( )
dc.contributor.authorSmyrlis, George ( )
dc.date.accessioned2021-08-26T17:23:06Z
dc.date.available2021-08-26T17:23:06Z
dc.date.issued2021-05-25
dc.identifier.citationPapanicolaou, V. G., Kallitsi, E., & Smyrlis, G. (2021). Entire solutions for the heat equation. Electronic Journal of Differential Equations, 2021(44), pp. 1-25.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14454
dc.description.abstract

We consider the solutions of the heat equation

tF = ∂2zF

which are entire in z and t (caloric functions). We examine the relation of the z-order and z-type of an entire caloric function F(t, z), viewed as function of z, to its t-order and t-type respectively, if it is viewed as function of t. Also, regarding the zeros zk(t) of an entire caloric function F(t, z), viewed as function of z, we show that the points (t, z) at which

F(t, z) = ∂zF(t, z) = 0

form a discrete set in ℂ2 and, then, we derive the t-evolution equations of zk(t). These are differential equations that hold for all but countably many ts in ℂ.

dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectEntire solutionen_US
dc.subjectHeat equationen_US
dc.subjectEntire caloric functionsen_US
dc.subjectOrderen_US
dc.subjectDynamics of the zerosen_US
dc.titleEntire solutions for the heat equationen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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