Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 68, 1998 - Issue 3-4
Submit an article Journal homepage
28
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Propagation of singularities phenomena for equations of tricome type

R. Payne Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL, 33124-4250 E-mail: [email protected]
Pages 195-206 | Received 01 Jan 1997, Published online: 02 May 2007

  • Agmon , S. , Nirenberg , L. and protter , M. H. 1953 . ‘A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type’ . Comma Pure Appl. Math. , 6 : 455 – 470 .
  • Beem , J.K. and Parker , P.E. 1983 . ;Klein-Gordon solvability and the geometry of geodesics . Pacific J.Math , 107 : 1 – 14 .
  • Bers , L. 1958 . “ Mathematical Aspects os Subsonic and Transonic Gas Dynamics ” . In Wiley New york
  • Duistermaat , J.J. and Hormander , L. 1972 . Fourier integral operators II . Acta Math , 128 : 183 – 269 .
  • Ellis , G.F.R. , Sumeruk , A. , Coule , D. and Hellaby , G. 1992 . Change of signature in classical relativity . Quantum Grav , 9 : 1535 – 1554 .
  • Frankl' , F.I. 1945 . On the problems of Chaplygin for mixed sub and supersonic flows . Isv.Akad.Nauk USSR Sere Mat. , 9 : 121 – 143 .
  • Friedrichs , K.O. 1958 . Symmetric positive linear differential equations’ . Comma Pure Appl.Math , 11 : 333 – 418 .
  • Germain , P. 1954 . Remarks on the theory of partial differential equations of mixed type and applications to the study of transonic flow . Comma Pure Appl.Math , 7 : 117 – 143 .
  • Gramchev , T.V. 1981 . An application of Airy functions to the Tricomi problem . Math Nachr , 102 : 169 – 181 .
  • Groothuizen , R.J.P. 1985 . Mixed eppiptic hyperbolic partial differential equations: a case study in Fourier integral operators . CWI Tract , 16 Centrum voor Wiskunde en informatica
  • Guderley , G. 1953 . “ ‘On the presence of shocks in mixed subsonic supersonic flow patterns’ ” . In Advances in Appl.Mech , 145 – 184 . New york : Academic press .
  • Hayward , S.A. 1992 . Signature change in general relativity . Class quantum Grav , 9 : 1851 – 1862 .
  • Hormander , L. 1976 . “ Linear Partial Differential Operators ” . Berlin : Springer–Verlag .
  • Hormander , L. 1971 . Fourier integral operators I . Acta Math. , 127 : 79 – 183 .
  • Hormander , L. 1985 . “ The Analysis of Linear Partial Differential Operators III,IV ” . Berlin : Springer-Verlag, .
  • Hormander , L. 1985 . The propagation of singularities for solutions of the Dirichlet problem . Proc. Sympos. Pure Math , 43 : 157 – 165 .
  • Imai , M. 1979 . Cauchy problems for the operator of Tricomi's type . Hokkaido Math , 8 : 126 – 143 .
  • Kossowski , M. and Kriele , M. 1993 . Smooth and discontinuous signature type change in general relativity’ . Class Quantum Grav , 10 : 2363 – 2371 .
  • Morawetz , C.S. 1966 . Mixed equations and transonic flow’ . Rend.Mat. , 25 : 1 – 28 .
  • Morawetz , C.S. 1970 . The Dirichlet problem for the Tricomi equation . Comm.Pure Appl.Math. , 23 : 587 – 601 .
  • Payne , K.R. 1996 . Interior regularity for the Dirichlet problem for the Tricomi equation . J.Math.Anal.Appl. , 199 : 271 – 292 .
  • Payne K.R. Propagation of singularities for solutions to the Dirichlet problem for equations of Tricomi type Rend. Sem. Mat. Univ. Polit. Torino to appear.
  • Payne K.R. Solvability theorems for linear equations of Tricomi type preprint n. 187/P Politecnico di Milano Berli 1996 submitted for publication.
  • Protter , M.H. 1953,1955 . Uniqueness theorems for the Tricomi problem I,II . J.Rat.Mech.Anal. , 2,4 : 107,721 – 114,732 .
  • Protter , M.H. 1954 . New boundary value problems for the wave equation and equations of mixed type . J.Rat.Mech.Anal , 3 : 435 – 446 .
  • Segala , F. 1985 . Parametrices for operators of Tricomi type . Ann.Mat.Pura.Appl. , 140 : 285 – 299 .
  • Scheurer , B. 1981 . Sur une perturbation singuliere d'operateurs differentiels elliptique hyperbolique . Comm.in Partial Differential Equation , 6 : 1235 – 1299 .
  • Taylor , M.E. 1981 . “ Pseudodifferential Operators ” . Princeton, , NJ : Princeton Univ. Press .
  • Tricomi , F. 1923 . Sulle equazioni lineari alle derivate parziali di secondo ondine, di tipo misto . Atti Naz Lincei Mem Cl.Fis.Mat.Nat , 14 ( 5 ) : 134 – 247 .
  • Weinstein , A. 1954 . The singular solutions and the Cauchy problem for generalized Tricomi equations . Comm.Pure Appl Math , 7 ( 5 ) : 105 – 116 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.