Nonlinear pseudoparabolic equations as singular limit of reaction–diffusion equations. (English) Zbl 1107.35061
Summary: A solution of a nonlinear pseudoparabolic equation is constructed as a singular limit of a sequence of solutions of quasilinear hyperbolic equations. If a system with cross diffusion, modelling the reaction and diffusion of two biological, chemical, or physical substances, is reduced then such an hyperbolic equation is obtained. For regular solutions even uniqueness can be shown, although the needed regularity can only be proved in two dimensions.
MSC:
| 35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
| 35K57 | Reaction-diffusion equations |
| 35K55 | Nonlinear parabolic equations |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
| 35K70 | Ultraparabolic equations, pseudoparabolic equations, etc. |
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