Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients |
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Authors: | Rico Zacher |
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Institution: | Martin-Luther University Halle-Wittenberg, Institute of Mathematics, Theodor-Lieser-Strasse 5, 06120 Halle, Germany |
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Abstract: | We investigate linear and quasilinear evolutionary partial integro-differential equations of second order which include time fractional evolution equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems. We also show that a maximum principle holds for such equations. |
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Keywords: | Integro-differential equation Quasilinear equation Fractional derivative Completely positive kernel Weak solution Energy estimates De Giorgi technique |
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