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Asymptotic behavior of solutions for parabolic operators of Leray-Lions type and measure data. (English) Zbl 1152.35323

Summary: Let Ω N be a bounded open set, N2, and let p>1; we study the asymptotic behavior with respect to the time variable t of the entropy solution of nonlinear parabolic problems whose model is

u t (x,t)-Δ p u(x,t)=μinΩ×(0,T),u(x,0)=u 0 (x)inΩ,

where T>0 is any positive constant, u 0 L 1 (Ω) a nonnegative function, and μ 0 (Q) is a nonnegative measure with bounded variation over Q=Ω×(0,T) which does not charge the sets of zero p-capacity; moreover, we consider μ that does not depend on time. In particular, we prove that solutions of such problems converge to stationary solutions.

35B40Asymptotic behavior of solutions of PDE
35K55Nonlinear parabolic equations
35R05PDEs with discontinuous coefficients or data