TY - JOUR
T1 - Smoothing effects of the initial-boundary value problem for logarithmic type quasilinear parabolic equations
AU - Nakao, Mitsuhiro
PY - 2018/6/15
Y1 - 2018/6/15
N2 - We give existence theorems of global solutions in Lloc ∞((0,∞);W0 1,∞) to the initial boundary value problem for quasilinear degenerate parabolic equations of the form ut−div{σ(|∇u|2)∇u}=0, where the class of σ(v2) includes the logarithmic case σ(|∇u|2)= log (1+|∇u|2) for a typical example. We assume that the initial data belong to W0 1,p0 ,p0≥2, or Lr,r≥1, and we derive precise estimates for ‖∇u(t)‖∞ near t=0.
AB - We give existence theorems of global solutions in Lloc ∞((0,∞);W0 1,∞) to the initial boundary value problem for quasilinear degenerate parabolic equations of the form ut−div{σ(|∇u|2)∇u}=0, where the class of σ(v2) includes the logarithmic case σ(|∇u|2)= log (1+|∇u|2) for a typical example. We assume that the initial data belong to W0 1,p0 ,p0≥2, or Lr,r≥1, and we derive precise estimates for ‖∇u(t)‖∞ near t=0.
KW - Moser's method
KW - Quasilinear parabolic equation
KW - Smoothing effects
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U2 - 10.1016/j.jmaa.2018.02.061
DO - 10.1016/j.jmaa.2018.02.061
M3 - Article
AN - SCOPUS:85042867170
VL - 462
SP - 1585
EP - 1604
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -