Our recent results on extended crystal PDE's and geometric theory on PDE's stability, are applied to the generalized $n$-d'Alembert PDE's, $(d'A)_n$, $n\ge 2$. We prove that these are extended crystal PDE's for any $n\ge 2$. For suitable $n$, $(d'A)_n$ becomes an extended $0$-crystal PDE and also a $0$-crystal PDE. An equation, having all the same smooth solutions of $(d'A)_n$, but without unstabilities at ''finite time'' is obtained for each $n\ge 2$.
On the extended crystal PDE's stability.I: The n-d'Alembert extended crystal PDE's / Prastaro, Agostino. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - STAMPA. - 1:204(2008), pp. 63-69. [10.1016/j.amc.2008.05.141]
On the extended crystal PDE's stability.I: The n-d'Alembert extended crystal PDE's
PRASTARO, Agostino
2008
Abstract
Our recent results on extended crystal PDE's and geometric theory on PDE's stability, are applied to the generalized $n$-d'Alembert PDE's, $(d'A)_n$, $n\ge 2$. We prove that these are extended crystal PDE's for any $n\ge 2$. For suitable $n$, $(d'A)_n$ becomes an extended $0$-crystal PDE and also a $0$-crystal PDE. An equation, having all the same smooth solutions of $(d'A)_n$, but without unstabilities at ''finite time'' is obtained for each $n\ge 2$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
