Entire solutions for the heat equation
Date
2021-05-25
Authors
Papanicolaou, Vassilis
Kallitsi, Eva
Smyrlis, George
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Entire solution, Heat equation, Entire caloric functions, Order, Dynamics of the zeros
Citation
Papanicolaou, V. G., Kallitsi, E., & Smyrlis, G. (2021). Entire solutions for the heat equation. <i>Electronic Journal of Differential Equations, 2021</i>(44), pp. 1-25.
Rights
Attribution 4.0 International