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Barbosa","submitted_at":"2016-03-19T15:26:27Z","abstract_excerpt":"We consider here the family of semilinear parabolic problems \\begin{equation*} \\begin{array}{rcl} \\left\\{ \\begin{array}{rcl} u_t(x,t)&=&\\Delta u(x,t) -au(x,t) + f(u(x,t)) ,\\,\\,\\ x \\in \\Omega_\\epsilon \\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\\,t>0\\,, \\\\ \\displaystyle\\frac{\\partial u}{\\partial N}(x,t)&=&g(u(x,t)), \\,\\, x \\in \\partial\\Omega_\\epsilon \\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\\,t>0\\,, \\end{array} \\right. \\end{array} \\end{equation*} where $ {\\Omega} $ is the unit square, $\\Omega_{\\epsilon}=h_{\\epsilon}(\\Omega)$ and $h_{\\epsilon}$ is a family of diffeomorphisms converging to the identity in the $C^1$-norm. 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Pereira, Marcone C. Pereira, Pricila S. Barbosa","submitted_at":"2016-03-19T15:26:27Z","abstract_excerpt":"We consider here the family of semilinear parabolic problems \\begin{equation*} \\begin{array}{rcl} \\left\\{ \\begin{array}{rcl} u_t(x,t)&=&\\Delta u(x,t) -au(x,t) + f(u(x,t)) ,\\,\\,\\ x \\in \\Omega_\\epsilon \\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\\,t>0\\,, \\\\ \\displaystyle\\frac{\\partial u}{\\partial N}(x,t)&=&g(u(x,t)), \\,\\, x \\in \\partial\\Omega_\\epsilon \\,\\,\\,\\mbox{and}\\,\\,\\,\\,\\,\\,t>0\\,, \\end{array} \\right. \\end{array} \\end{equation*} where $ {\\Omega} $ is the unit square, $\\Omega_{\\epsilon}=h_{\\epsilon}(\\Omega)$ and $h_{\\epsilon}$ is a family of diffeomorphisms converging to the identity in the $C^1$-norm. 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