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dc.contributor.authorPapanicolaou, Vassilis ( Orcid Icon 0000-0001-5405-7297 )
dc.contributor.authorKallitsi, Eva ( )
dc.contributor.authorSmyrlis, George ( )
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

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.format.extent25 pages
dc.format.medium1 file (.pdf)
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.subjectDynamics of the zerosen_US
dc.titleEntire solutions for the heat equationen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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