Reduction of the Number of Variables in Systems of Partial Differential Equations, with Auxiliary Conditions

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Previous article Next article Reduction of the Number of Variables in Systems of Partial Differential Equations, with Auxiliary ConditionsM. J. Moran and R. A. GaggioliM. J. Moran and R. A. Gaggiolihttps://doi.org/10.1137/0116018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff, Hydrodynamics: A study in logic, fact and similitude, Revised ed, Princeton Univ. Press, Princeton, N.J., 1960xi+184 pp. (1 plate) MR0122193 0095.20303 Google Scholar[2] A. J. A. Morgan, The reduction by one of the number of independent variables in some systems of partial differential equations, Quart. J. Math., Oxford Ser. (2), 3 (1952), 250–259 MR0056183 0047.33403 CrossrefGoogle Scholar[3] Aristotle D. Michal, Differential invariants and invariant partial differential equations under continuous transformation groups in normed linear spaces, Proc. Nat. Acad. Sci. U. S. A., 37 (1951), 623–627 MR0043376 0054.04904 CrossrefISIGoogle Scholar[4] M. J. Moran, Masters Thesis, A unification of dimensional and similarity analysis via group theory, Doctoral dissertation, University of Wisconsin, Madison, 1967 Google Scholar[5] R. Manohar, Some similarity solutions of partial differential equations of boundary layer, Tech. Summary Rep., 375, Mathematics Research Center, University of Wisconsin, Madison, 1963 Google Scholar[6] Arthur G. Hansen, Similarity analyses of boundary value problems in engineering, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964xiv+114 MR0178596 0137.22603 Google Scholar[7] Luther Pfahler Eisenhart, Continuous groups of transformations, Dover Publications Inc., New York, 1961ix+301 MR0124008 0096.02103 Google Scholar[8] G. F. D. Duff, Partial differential equations, Mathematical expositions no. 9, University of Toronto Press, Toronto, 1956x+248 MR0078550 0071.30903 Google Scholar[9] R. A. Gaggioli and , M. J. Moran, Group theoretic techniques for the similarity solution of systems of partial differential equations with auxiliary conditions, Tech. Summary Rep., 693, Mathematics Research Center, University of Wisconsin, Madison, 1966 Google Scholar[10] Hermann Schlichting, Boundary layer theory, Translated by J. Kestin. 4th ed. McGraw-Hill Series in Mechanical Engineering, McGraw-Hill Book Co., Inc., New York, 1960xx+647 MR0122222 0096.20105 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Group method analysis for blood‐Mn‐ZnFe 2 O 4 flow and heat transfer under ferrohydrodynamics through a stretched cylinderMathematical Methods in the Applied Sciences, Vol. 28 | 21 June 2022 Cross Ref Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary LayerMathematical Journal of Interdisciplinary Sciences, Vol. 9, No. 2 | 8 June 2021 Cross Ref Forward scattering for non-linear wave propagation in (3 + 1)-dimensional Jimbo-Miwa equation using singular manifold and group transformation methodsWaves in Random and Complex Media, Vol. 9 | 21 July 2020 Cross Ref Advanced Ground Truth Multimodal Imaging Using Time Reversal (TR) Based Nonlinear Elastic Wave Spectroscopy (NEWS): Medical Imaging Trends Versus Non-destructive Testing ApplicationsRecent Advances in 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GaggioliSIAM Journal on Mathematical Analysis, Vol. 1, No. 1 | 17 February 2012AbstractPDF (334 KB)Optimized excitation sources and exact solutions for ultrasonic field propagation in a nonlinear medium with hysteretic behaviorIEEE Ultrasonics Symposium, 2004 Cross Ref Motion of an electric arc in a transverse magnetic field.AIAA Journal, Vol. 6, No. 10 | 1 Oct 1968 Cross Ref Similarity analyses via group theory.AIAA Journal, Vol. 6, No. 10 | 1 Oct 1968 Cross Ref Erratum: "Boundary-Layer Transition OD Ablating Conesat Speeds up to 7 km/secAIAA Journal, Vol. 6, No. 10 | 1 Oct 1968 Cross Ref Erratum: "Symptomatic Behavior of an Electric Arc with a Superimposed Flow"AIAA Journal, Vol. 6, No. 10 | 1 Oct 1968 Cross Ref Chapter 2: Applications of Modern AlgebraNonlinear Partial Differential Equations in Engineering | 1 Jan 1965 Cross Ref Volume 16, Issue 1| 1968SIAM Journal on Applied Mathematics1-254 History Submitted:03 February 1967Published online:12 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116018Article page range:pp. 202-215ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics