TY - JOUR
T1 - Sobolev regularity for t > 0 in quasilinear parabolic equations
AU - Milani, Albert
PY - 2001
Y1 - 2001
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.
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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
AN - SCOPUS:0039840070
SN - 0025-584X
VL - 231
SP - 113
EP - 127
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
ER -