### Abstract

We establish a regularity property for the solutions to the quasilinear parabolic initial-boundary value problem (1.4) below, showing that for t > 0 they belong to the same space to which the solutions of the second order hyperbolic problem (1.5), which is a singular perturbation of (1.4), belong. This result provides another illustration of the asymptotically parabolic nature of problem (1.5), and would be needed to establish the diffusion phenomenon for quasilinear dissipative wave equations in Sobolev spaces.

Original language | English |
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Pages (from-to) | 113-127 |

Number of pages | 15 |

Journal | Mathematische Nachrichten |

Volume | 231 |

DOIs | |

Publication status | Published - Jan 1 2001 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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**Sobolev regularity for t > 0 in quasilinear parabolic equations.** / Milani, Albert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Sobolev regularity for t > 0 in quasilinear parabolic equations

AU - Milani, Albert

PY - 2001/1/1

Y1 - 2001/1/1

N2 - We establish a regularity property for the solutions to the quasilinear parabolic initial-boundary value problem (1.4) below, showing that for t > 0 they belong to the same space to which the solutions of the second order hyperbolic problem (1.5), which is a singular perturbation of (1.4), belong. This result provides another illustration of the asymptotically parabolic nature of problem (1.5), and would be needed to establish the diffusion phenomenon for quasilinear dissipative wave equations in Sobolev spaces.

AB - We establish a regularity property for the solutions to the quasilinear parabolic initial-boundary value problem (1.4) below, showing that for t > 0 they belong to the same space to which the solutions of the second order hyperbolic problem (1.5), which is a singular perturbation of (1.4), belong. This result provides another illustration of the asymptotically parabolic nature of problem (1.5), and would be needed to establish the diffusion phenomenon for quasilinear dissipative wave equations in Sobolev spaces.

UR - http://www.scopus.com/inward/record.url?scp=0039840070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039840070&partnerID=8YFLogxK

U2 - 10.1002/1522-2616(200111)231:1<113::AID-MANA113>3.0.CO;2-M

DO - 10.1002/1522-2616(200111)231:1<113::AID-MANA113>3.0.CO;2-M

M3 - Article

VL - 231

SP - 113

EP - 127

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

ER -