Geodesic
The heat equation and the shrinking
Electronic journal of differential equations, Tome 2003 (2003)
This article concerns the Cauchy problem for the partial differential equation

$ \partial_1 u(t,x)-a\partial_2^2 u(t,x) =f(t,x,\partial_2^p u(\mu(t)t,x),\partial_2^q u(t,\nu(t)x))\,. $

Here $t$ and $x$ are real variables, $p$ and $q$ are positive integers greater than 1, and the shrinking factors $\mu(t), \nu(t)$ are positive-valued functions such that their suprema are less than 1.
Classification : 35K05, 35K55, 35R10, 49K25
Keywords: partial differential equation, heat equation, shrinking, delay 
@article{EJDE_2003__2003__a0,
     author = {Kawagishi,  Masaki and Yamanaka,  Takesi},
     title = {The heat equation and the shrinking},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1039.35048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a0/}
}
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Kawagishi,  Masaki; Yamanaka,  Takesi. The heat equation and the shrinking. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a0/