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Sobolev Regularity for t > 0 in Quasilinear Parabolic Equations
Author(s) -
Milani Albert
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200111)231:1<113::aid-mana113>3.0.co;2-m
Subject(s) - mathematics , sobolev space , mathematical analysis , parabolic partial differential equation , dissipative system , perturbation (astronomy) , boundary value problem , singular perturbation , initial value problem , pure mathematics , partial differential equation , physics , quantum mechanics
We establish a regularity property for the solutions to the quasilinear parabolicinitial‐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 ofproblem (1.5), and would be needed to establish the diffusion phenomenon for quasilinear dissipative wave equations in Sobolev spaces.