Entire solutions for the heat equation
| dc.contributor.author | Papanicolaou, Vassilis (  0000-0001-5405-7297 ) | |
| dc.contributor.author | Kallitsi, Eva ( ) | |
| dc.contributor.author | Smyrlis, George ( ) | |
| dc.date.accessioned | 2021-08-26T17:23:06Z | |
| dc.date.available | 2021-08-26T17:23:06Z | |
| dc.date.issued | 2021-05-25 | |
| dc.identifier.citation | Papanicolaou, 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.issn | 1072-6691 | |
| dc.identifier.uri | https://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.format | Text | |
| dc.format.extent | 25 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.language.iso | en | en_US |
| dc.publisher | Texas State University, Department of Mathematics | en_US |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Entire solution | en_US |
| dc.subject | Heat equation | en_US |
| dc.subject | Entire caloric functions | en_US |
| dc.subject | Order | en_US |
| dc.subject | Dynamics of the zeros | en_US |
| dc.title | Entire solutions for the heat equation | en_US |
| dc.type | publishedVersion | |
| txstate.documenttype | Article | |
| dc.rights.license |  This work is licensed under a Creative Commons Attribution 4.0 International License. |
