Description

• Title:
  Topological characteristic of fully nonlinear parabolic boundary value problems
• Creator:
  Skrypnik, Igor V.;
  Romanenko, Igor B.
• Description:
  A general nonlinear initial boundary value problem $$ \align \frac{\partial u}{\partial t} - F(x,t,u,D^{1}u,\dots, D^{2m}u)&=f(x,t), \tag 1 \\ &\hskip -30pt (x,t)\in Q_{T}\equiv \Omega\times (0,T), \\ G_{j}(x,t,u,\dots, D^{m_{j}}u)&=g_{j}(x,t), \tag 2\\ &\hskip-30pt (x,t)\in S_{T}\equiv \partial\Omega\times (0,T), j=\overline{1,m}, \\ u(x,0)=h(x),\quad& x\in\Omega \tag 3 \endalign $$ is being considered, where $\Omega$ is a bounded open set in $\R^n$ with sufficiently smooth boundary. The problem (1)-(3) is then reduced to an operator equation $Au=0$, where the operator $A$ satisfies (S)$_+$ condition. The local and global solvability of the problem (1)-(3) are achieved via topological methods developed by the first author. Further applications involving the convergence of Galerkin approximations are also given.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2004.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 23, No 1 (March 2004); 1 - 31;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2004.001/9214
• Subject:
  Parabolic problems;
  nonlinear boundary condition;
  fully nonlinear parabolic equation;
  operator of type (S)$_ $;
  Galerkin approximations;
  Primary 35K55;
  Secondary 35K30;
  35K35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2004.001
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other