Geodesic
The heat equation and the shrinking
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Kawagishi, Masaki and Yamanaka, Takesi},
     title = {The heat equation and the shrinking},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a100/}
}
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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__a100/