Description

• Title:
  Quasilinear parabolic equations with nonlinear monotone boundary conditions
• Creator:
  Lin, Chin-Yuan
• Description:
  Of concern is the following quasilinear parabolic equation with a nonlinear monotone boundary condition: $$ \cases \displaystyle u_{t} (x, t) = \frac{\partial \alpha (x, u_{x})}{\partial x} + g(x, u), \quad (x, t) \in (0, 1) \times (0, \infty), \\ (\alpha (0, u_{x}(0, t)), - \alpha (1, u_{x}(1, t))) \in \beta (u(0, t), u(1, t)), \\ u(x, 0) = u_{0}(x). \endcases \tag $*$ $$ Here $ \beta $ is a maximal monotone graph in $ {\mathbb R} \times {\mathbb R}$, which contains the origin $(0, 0)$. It is showed that (*) has a unique strong solution $ u $, with the property that $$ \sup_{t \in [0, T]}\|u(x, t)\|_{C^{1+ \nu}[0, 1]} $$ is uniformly bounded for $ 0 < \nu < 1 $ and finite $ T > 0 $.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  1999.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 13, No 2 (June 1999); 235 - 249;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.012/10035
• Subject:
  m-dissipative operators;
  method of lines;
  35A05;
  35B35;
  35B65;
  47H17;
  47H20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.012
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other