Abstract:
The asymptotic behavior of the solution to the Cauchy problem
for an inhomogeneous heat equation with a right-hand side
that has a self-similar asymptotic behavior at infinity
is investigated.
Using the auxiliary parameter method and
the regularization of singularities of the integrands,
we obtain an asymptotic approximation of the solution
in the form of an Erdélyi series
in half-integer powers of the time variable
with coefficients depending on the self-similar variable
and the logarithm of time.
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