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Jakobsen, F\\'elix del Teso, J{\\o}rgen Endal","submitted_at":"2017-06-16T15:02:52Z","abstract_excerpt":"We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\\partial_tu-\\mathfrak{L}^{\\sigma,\\mu}[\\varphi(u)]=g(x,t)\\quad\\quad\\text{in}\\quad\\quad \\mathbb{R}^N\\times(0,T),$$ where $\\varphi$ is merely continuous and nondecreasing and $\\mathfrak{L}^{\\sigma,\\mu}$ is the generator of a general symmetric L\\'evy process. This means that $\\mathfrak{L}^{\\sigma,\\mu}$ can have both local and nonlocal parts like e.g. $\\mathfrak{L}^{\\sigma,\\mu}=\\Delta-(-\\Delta)^{\\frac12}$. 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