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Partielle Differentialgleichungen vom gemischten Typus

In: Repertorium der Theorie der Differentialgleichungen

Author

Listed:
  • Francesco Giacomo Tricomi

    (Accademico Linceo)

Abstract

Zusammenfassung Wir wissen schon (Abschn. 2.1), daß eine quasilineare partielle Differentialgleichung der Form (4.1.1) $$A\left( {x,y} \right){z_{xx}} + 2B\left( {x,y} \right){z_{xx}} + C\left( {x,y} \right){z_{yy}} = f{\rm{(}}x,y,z,{z_x},{z_y}) $$ vom gemischten Typus ist, falls ihre Diskriminante (4.1.2) $$\Delta \left( {x,y} \right) = {B^2}\left( {x,y} \right) - A\left( {x,y} \right)\,C\left( {x,y} \right) $$ in dem uns interessierenden Bereich B weder stets positiv, noch stets negativ, noch identisch Null ist. Es handelt sich also um Gleichungen, für welche die Diskriminante Δ — ohne identisch Null zu sein — auf einer gewissen „parabolischen Linie“ c von B verschwindet.

Suggested Citation

  • Francesco Giacomo Tricomi, 1968. "Partielle Differentialgleichungen vom gemischten Typus," Springer Books, in: Repertorium der Theorie der Differentialgleichungen, chapter 0, pages 133-161, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-88092-6_4
    DOI: 10.1007/978-3-642-88092-6_4
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