This paper is the second part of a work devoted to the algebraic topological characterization of PDE's stability and its relation with an important class of PDE's called {\em extended crystals PDE's}. In fact, their integral bordism groups can be considered extensions of subgroups of crystallographic groups. This allows us to identify a characteristic class that measures the obstruction to the existence of global solutions. In part I we identified criteria to recognize PDE's that are stable (in extended Ulam sense) and in their regular smooth solutions do not occur finite time unstabilities, ({\em stable extended crystal PDE's}). Here we study in some details a new PDE encoding anisotropic incompressible magnetohydrodynamics. A stable extended crystal MHD-PDE's is obtained where in its smooth solutions do not occurr unstabilities in finite times. These results are considered first for systems without body energy source and after by introducing also a contribution by energy source in order to take into account of nuclear energy production. A condition in order solutions satisfy the second principle of thermodynamics is given.

Extended crystal PDE's stability.II: The extended crystal MHD-PDE's / Prastaro, Agostino. - In: MATHEMATICAL AND COMPUTER MODELLING. - ISSN 0895-7177. - ELETTRONICO. - 9-10:49(2009), pp. 1781-1801. [10.1016/j.mcm.2008.07.021]

Extended crystal PDE's stability.II: The extended crystal MHD-PDE's

PRASTARO, Agostino
2009

Abstract

This paper is the second part of a work devoted to the algebraic topological characterization of PDE's stability and its relation with an important class of PDE's called {\em extended crystals PDE's}. In fact, their integral bordism groups can be considered extensions of subgroups of crystallographic groups. This allows us to identify a characteristic class that measures the obstruction to the existence of global solutions. In part I we identified criteria to recognize PDE's that are stable (in extended Ulam sense) and in their regular smooth solutions do not occur finite time unstabilities, ({\em stable extended crystal PDE's}). Here we study in some details a new PDE encoding anisotropic incompressible magnetohydrodynamics. A stable extended crystal MHD-PDE's is obtained where in its smooth solutions do not occurr unstabilities in finite times. These results are considered first for systems without body energy source and after by introducing also a contribution by energy source in order to take into account of nuclear energy production. A condition in order solutions satisfy the second principle of thermodynamics is given.
2009
Stability in PDE's geometry; Integral bordism groups in PDE's; Singular PDE's; Geometry of MHD PDE's.
01 Pubblicazione su rivista::01a Articolo in rivista
Extended crystal PDE's stability.II: The extended crystal MHD-PDE's / Prastaro, Agostino. - In: MATHEMATICAL AND COMPUTER MODELLING. - ISSN 0895-7177. - ELETTRONICO. - 9-10:49(2009), pp. 1781-1801. [10.1016/j.mcm.2008.07.021]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/36309
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 5
social impact