Abstract
We establish well-posed solvability of the Cauchy problem for the Shilov parabolic equations with time-dependent coefficients whose initial data are tempered distributions. For a certain class of equations we state necessary and sufficient conditions for unique solvability of the Cauchy problem whose properties with respect to the spatial variable are typical for a fundamental solution. The results are characterized only by the order and the parabolicity exponent.
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Litovchenko, V.A. The Cauchy Problem for Shilov Parabolic Equations. Siberian Mathematical Journal 45, 669–679 (2004). https://doi.org/10.1023/B:SIMJ.0000035831.63036.bb
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DOI: https://doi.org/10.1023/B:SIMJ.0000035831.63036.bb