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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Acknowledgments
The publication has been prepared with the support of the ‘RUDN University Program 5-100’.
Disclosure statement
No potential conflict of interest was reported by the author(s).