Title

Nonlinear degenerate parabolic equations with singular lower-order term

Abstract

We use variational methods to study the nonexistence of positive solutions for the following nonlinear parabolic partial differential equations:{∂u/∂t = δ(um) + V (x)um in ω × (0, T), u(x, 0) = u0(x) ≥ 0 in ω, u(x, t) = 0 on ∂ω × (0, T), and {∂u/∂t = δpu + V (x)up-1 in ω × (0, T), u(x, 0) = u0(x) ≥0 in ω, u(x, t) = 0 on ∂ω × (0, T), where 0 < m < 1, 1 < p < 2, V ∈ L1loc(ω) and ω is a bounded domain with smooth boundary in ℝN.

Publication Title

Advances in Differential Equations

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