The Absence of Positive Global Periodic Solution of a Second-Order Semi Linear Parabolic Equation With Time-Periodic Coefficients

Year 2024, Volume: 14 Issue: 2, 20 - 35, 31.07.2024

Shirmayil G. Bagyrov

Abstract

Second order semilinear parabolic equation ∂u∂t = div(A(x, t)∇u) + h(x, t, u)
with time-periodic coefficients is considered in domain Ω × (−∞, +∞), where Ω is the
exterior of a compact set in Rnx. Depending on the behavior of the function h(x, t, u)
at infinity, the conditions are found under which the positive periodic solution does not
exist.

Keywords

semilinear parabolic equation , periodic solution , nonexistence of global solutions.

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