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R^N\\times(0,\\infty),\\\\ u(x,0) = u_0(x)\\quad& \\mbox{in}\\quad \\mathbb R^N, \\end{cases} \\end{align} where $p>1$, $u_0\\ge0$ and bounded and $$ \\mathcal{L} u(x,t)=\\int J(x-y)\\left(u(y,t)-u(x,t)\\right)\\,dy $$ with $J\\in C_0^{\\infty}(\\mathbb R^N)$, radially symmetric, $J\\geq 0$ with $\\int J=1$.\n  Our assumption on the initial datum is that $0\\le u_0\\in L^\\infty(\\mathbb R^N)$ and $$ 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