### Abstract

Original language | English |
---|---|

Pages (from-to) | 1285-1299 |

Number of pages | 15 |

Journal | Applicable Analysis |

Volume | 85 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2006 |

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### Keywords

- Pseudo-parabolic equations
- Galerkin’s method
- Reaction-diffusion equations

### Cite this

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*Applicable Analysis*, vol. 85, no. 10, pp. 1285-1299. https://doi.org/10.1080/00036810600871909

**Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations.** / Ptashnyk, Mariya (Lead / Corresponding author).

Research output: Contribution to journal › Article

TY - JOUR

T1 - Nonlinear pseudoparabolic equations as singular limit of reaction-diffusion equations

AU - Ptashnyk, Mariya

PY - 2006/10

Y1 - 2006/10

N2 - In this article, 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.

AB - In this article, 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.

KW - Pseudo-parabolic equations

KW - Galerkin’s method

KW - Reaction-diffusion equations

U2 - 10.1080/00036810600871909

DO - 10.1080/00036810600871909

M3 - Article

VL - 85

SP - 1285

EP - 1299

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 10

ER -