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Second-order type-changing evolution equations with first-order intermediate equations |
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| Authors: | Jeanne Clelland Marek Kossowski |
| Institution: | a Department of Mathematics, University of Colorado, Campus Box 395, Boulder, CO 80309-0395, USA b Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA c Department of Mathematics, University of Hawaii at Manoa, 2565 McCarthy Mall, Honolulu, HI 96822-2273, USA |
| Abstract: | This paper presents a partial classification for C∞ type-changing symplectic Monge-Ampère partial differential equations (PDEs) that possess an infinite set of first-order intermediate PDEs. The normal forms will be quasi-linear evolution equations whose types change from hyperbolic to either parabolic or to zero. The zero points can be viewed as analogous to singular points in ordinary differential equations. In some cases, intermediate PDEs can be used to establish existence of solutions for ill-posed initial value problems. |
| Keywords: | primary 58J70 35A30 secondary 35L67 35L65 35L70 35L90 |
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