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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.

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