Weighted Estimates for the Solutions of Non-linear Partial Differential Equations

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The project aims to investigate weighted estimates for some class of integral operators that arise in connection to solving linear and non-linear partial differential equations. The information provided by these estimates are how one can control the hight and width of a solution, as well as where it is mainly concentrated, by the corresponding properties of the right hand side and/or the initial data of the equation. The specific applications concern estimates for the solutions of non-linear heat-type and wave-type equations.