Celebratio Mathematica — Morawetz

Transonic flow and
mixed-type partial differential equations

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C. S. Morawetz: “On the non-existence of continuous transonic flows past profiles, III,” Comm. Pure Appl. Math. 11 : 1 (1958), pp. 129–144. MR 96478 article

C. S. Morawetz: “The mathematical approach to the sonic barrier,” Bull. Am. Math. Soc. (N.S.) 6 : 2 (1982), pp. 127–145. Josiah Willard Gibbs lecture presented at AMS meeting, San Francisco, 7 January 1981. MR 640941 Zbl 0506.76064 article

D. Lupo, C. S. Morawetz, and K. R. Payne: “On closed boundary value problems for equations of mixed elliptic-hyperbolic type,” Comm. Pure Appl. Math. 60 : 9 (2007), pp. 1319–1348. An erratum to this article was published in Comm. Pure Appl. Math. 61:4 (2008). MR 2337506 Zbl 1125.35066 article

For partial differential equations of mixed elliptic-hyperbolic type we prove results on existence and existence with uniqueness of weak solutions for closed boundary value problems of Dirichlet and mixed Dirichlet-conormal types. Such problems are of interest for applications to transonic flow and are overdetermined for solutions with classical regularity. The method employed consists in variants of the \( a - b - c \) integral method of Friedrichs in Sobolev spaces with suitable weights. Particular attention is paid to the problem of attaining results with a minimum of restrictions on the boundary geometry and the form of the type change function. In addition, interior regularity results are also given in the important special case of the Tricomi equation.

Daniela Lupo	Related
Kevin Ray Payne	Related

Transonic flow andmixed-type partial differential equations

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Transonic flow and
mixed-type partial differential equations