Abstract
ABSTRACT We deal with m-component vector-valued solutions to the Cauchy problem for a linear both homogeneous and nonhomogeneous weakly coupled second-order parabolic system in the layer . We assume that coefficients of the system are real and depending only on t, and . The homogeneous system is considered with initial data in , . For the nonhomogeneous system we suppose that the initial function is equal to zero and the right-hand side belongs to , . Explicit formulas for the sharp coefficients in pointwise estimates for solutions to these problems and their directional derivative are obtained.
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