On the singular PDE's geometry and boundary value problems

References

• Gromov , M . 1986 . Partial Differential Relations , Berlin : Springer-Verlag .
   Google Scholar
• Lychagin , V and Prástaro , A . 1994 . Singularities of Cauchy data, characteristics, cocharacteristics and integral cobordism . Diff. Geom. Appl. , 4 : 287 – 300 .
   Google Scholar
• Prástaro (ed.) , A . 1985 . “ Dynamic Conservation Laws ” . In Geometrodynamics Proceedings 1985 , Singapore : World Scientific Publishing Co. .
   Google Scholar
• Prástaro , A . 1991 . Cobordism of PDE's . Boll. Un. Mat. Ital. , 30 ( 5-B ) : 977 – 1001 .
   Google Scholar
• Prástaro , A . 1991 . Quantum geometry of PDE's . Rep. Math. Phys. , 30 ( 3 ) : 273 – 354 .
   Google Scholar
• Prástaro , A . 1996 . Geometry of PDE's and Mechanics , Singapore : World Scientific Publishing Co. .
   Google Scholar
• Prástaro , A . 1996 . (Co)bordisms in PDE's and quantum PDE's . Rep. Math. Phys. , 38 ( 3 ) : 443 – 455 .
   Google Scholar
• Prástaro , A . 1998 . Quantum and integral (co)bordism groups in partial differential equations . Acta Appl. Math. , 51 ( 3 ) : 243 – 302 .
   Google Scholar
• Prástaro , A . 1999 . (Co)bordism groups in PDE's . Acta Appl. Math. , 59 ( 2 ) : 111 – 202 .
   Google Scholar
• Prástaro , A . 2004 . Quantized Partial Differential Equations , River Edge, NJ : World Scientific Publishing Co. .
   Google Scholar
• Prástaro , A . 2006 . Geometry of PDE's. I: Integral bordism groups in PDE's . J. Math. Anal. Appl. , 319 : 547 – 566 .
   Google Scholar
• Prástaro , A . 2006 . Geometry of PDE's. II: Variational PDE's and integral bordism groups . J. Math. Anal. Appl. , 321 : 930 – 948 .
   Google Scholar
• Prástaro , A . 2008 . Geometry of PDE's. IV: Navier–Stokes equation and integral bordism groups . J. Math. Anal. Appl. , 338 ( 2 ) : 1140 – 1151 .
   Google Scholar
• Prástaro , A . 2007 . (Un)stability and bordism groups in PDE's . Banach J. Math. Anal. , 1 ( 1 ) : 139 – 147 .
   Google Scholar
• A. Prástaro, Extended crystal PDE's arXiv:0811.3693v2[math.AT] (submitted for publication)
   Google Scholar
• A. Prástaro, Extended crystal PDE's stability. I: The general theory, Math. Comput. Modelling 49(9–10) (2009), pp. 1759–1780
   Google Scholar
• A. Prástaro, Extended crystal PDE's stability. II: The extended crystal MHD-PDE's, Math. Comput. Modelling 49(9–10) (2009), pp. 1781–1801
   Google Scholar
• Prástaro , A . 2008 . On the extended crystal PDE's stability. I: The n-d'Alembert extended crystal PDE's . Appl. Math. Comput. , 204 ( 1 ) : 63 – 69 .
   Google Scholar
• Prástaro , A . 2008 . On the extended crystal PDE's stability. II: Entropy-regular-solutions in MHD-PDE's . Appl. Math. Comput. , 204 ( 1 ) : 82 – 89 .
   Google Scholar
• Goldschmidt , H . 1967 . Integrability criteria for systems of non-linear partial differential equations . J. Differential Geom. , 1 : 269 – 307 .
   Google Scholar
• Boardman , JM . 1967 . Singularities of differentiable maps . Publ. Math. I.H.E.S. , 33 : 21 – 57 .
   Google Scholar
• Golubitsky , M and Guillemin , V . 1973 . Stable Mappings and Their Singularities , New York : Springer-Verlag .
   Google Scholar
• Hirsh , MW . 1976 . Differential Topology , Berlin : Springer-Verlag .
   Google Scholar
• Madsen , IB and Milgram , RJ . 1979 . “ The Classifying Spaces for Surgery and Bordism of Manifolds ” . In Annals of Mathematical Studies , NJ : Princeton University Press .
   Google Scholar
• Milnor , J and Stasheff , J . 1974 . “ Characteristic Classes ” . In Annals of Mathematical Studies , Vol. 76 , Princeton : Princeton University Press .
   Google Scholar
• Rudyak , YB . 1998 . On Thom Spectra, Orientability and Cobordism , Berlin : Springer-Verlag .
   Google Scholar
• Stong , RE . 1968 . “ Notes on Bordism Theories ” . In Annals of Mathematics Studies , Princeton : Princeton University Press .
   Google Scholar
• Switzer , R . 1975 . Algebraic Topology-Homotopy and Homology , Berlin : Springer-Verlag .
   Google Scholar
• Thom , R . 1954 . Quelques propriété globales des variétés différentieles . Commen. Math. Helv. , 28 : 17 – 86 .
   Google Scholar
• Thom , R . 1954 . Remarques sur les problemes comportant des inéqualities différentielles globales . Bull. Soc. Math. France. , 87 : 455 – 468 .
   Google Scholar
• Thom , R . 1955–56 . Les singularités des applications differentiables . Ann. Inst. Fourier , 6 : 43 – 87 .
   Google Scholar
• Wall , CTC . 1960 . Determination of the cobordism ring . Ann. Math. , 72 : 292 – 311 .
   Google Scholar
• C.T.C Wall, Surgery on Compact Manifolds, London Math. Soc. Monographs 1, Academic Press, New York, 1970; 2nd edn (ed. A.A. Ranicki), Amer. Math. Soc. Surveys and Monographs 69, A.M.S., 1999
   Google Scholar
• Bryant , RL , Chern , SS , Gardner , RB , Goldschmidt , HL and Griffiths , PA . 1991 . Exterior Differential Systems , New York : Springer-Verlag .
   Google Scholar
• Cappel , S , Ranicki , A and Rosenberg (eds.) , J . 1999 . Surveys on Surgery Theory: Volume 1 , Princeton, New Jersey : Papers dedicated to C. T. C. Wall, Princeton University Press .
   Google Scholar
• Goldschmidt , H and Spencer , D . 1977 . Submanifolds and Over-determined Differential Operators , 319 – 356 . Cambridge : Complex Analysis & Algebraic Geometry, Cambridge University Press .
   Google Scholar
• Krasilśhchik , IS , Lychagin , V and Vinogradov , AM . 1986 . Geometry of Jet Spaces and Nonlinear Partial Differential Equations , Amsterdam : Gordon and Breach Science Publishers S.A. .
   Google Scholar
• Kuranishi , M . 1957 . On the Cartan prolongation theorem of exterior differential systems . Amer. J. Math. , 79 ( 1 ) : 1 – 47 .
   Google Scholar
• Agarwal , RP and Prástaro , A . 2007 . Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory . Adv. Math. Sci. Appl. , 17 ( 1 ) : 239 – 266 .
   Google Scholar
• Agarwal , RP and Prástaro , A . 2007 . Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's . Adv. Math. Sci. Appl. , 17 ( 1 ) : 267 – 281 .
   Google Scholar
• Agarwal , RP and Prástaro , A . 2008 . Singular PDE's geometry and boundary value problems . J. Nonlinear Conv. Anal. , 9 ( 3 ) : 417 – 460 .
   Google Scholar
• Agarwal , RP and O'Regan , D . 2001 . Singular problems on the infinite interval modelling phenomena in draining flows . IMA J. Appl. Math. , 66 : 621 – 635 .
   Web of Science ®Google Scholar
• Agarwal , RP . “ Singular boundary value problems with real world applications ” . In preprint (2008), Lecture delivered Department of Methods and Mathematical Models for Applied Sciences , Roma, , Italy : University of Roma ‘La Sapienza’ . May 20
   Google Scholar