Description

• Title:
  Nonlinear delay reaction-diffusion systems with nonlocal initial conditions having affine growth
• Creator:
  Burlică, Monica-Dana;
  Roşu, Daniela
• Description:
  We consider a class of abstract evolution reaction-diffusion systems with delay and nonlocal initial data of the form $$ \begin{cases} \displaystyle u'(t)\in Au(t)+F(t,u_t,v_t)&\text{for } t\in \mathbb{R}_+,\\ v'(t)\in Bv(t)+G(t,u_t,v_t) & \text{for } t\in \mathbb{R}_+,\\ u(t)=p(u,v)(t)& \text{for } t\in [-\tau_1,0],\\ v(t)=q(u,v)(t)& \text{for } t\in [-\tau_2,0], \end{cases} $$ where $\tau_i\geq 0$, $i=1,2$, $A$ and $B$ are two $m$-dissipative operators acting in two Banach spaces, the perturbations $F$ and $G$ are continuous, while the history functions $p$ and $q$ are nonexpansive functions with affine growth. We prove an existence result of $C^0$-solutions for the above problem and we give an example to illustrate the effectiveness of our abstract theory.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.04.04
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 48, No 2 (December 2016); 371 - 392;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.027/8063 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.027/8064
• Subject:
  Differential delay evolution systems;
  nonlocal delay initial condition;
  metric fixed point arguments;
  nonlinear reaction-diffusion systems;
  Primary;
  34G25;
  34K30;
  Secondary;
  35K55;
  35K57;
  47H06
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.027
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other