| Abstract |
Consider the linear parabolic type equation with multivariate time
, (1)
where - space of time variable, – - measured of the Euclid space of vectors
– operator of Laplase; – set function.
Assumption that the is - periodicity on and almost periodic on with - almost period even with respect to , also satisfy on and condition of Gelder with exponents and accordingly.
Problem. Find sufficient conditions existence and uniqueness multiperiodical on and almost periodic on solution of parabolic type equation (1), which satisfy border condition
, (2)
where function - - periodicity on and almost periodic on . Among of the boundary value problem which set all along the space, considerable interes represent of half-space boundary vale problem which bring to study periodic and almost periodic solutions of parabolic equation [1], [2].
Develop idea of work [3] is found some condition of quality bound with multiperiodic and almost periodic of variable part of the fundamental solution and get sufficient conditions existence and uniqueness multiperiodical on and almost periodic on solution of the first boundary value problem (1) – (2).
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