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

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.

References

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