RT Book, Section
T1 On the limit of solutions of ut=Δum as m→∞
A1 Bénilan, Philippe
A1 Boccardo, L.
A1 Herrero, Miguel A.
AB Let f∈L1(RN), N≥1, f≥0, and consider the Cauchy problem ut=Δum on ]0,∞[×RN, u(0,⋅)=f on RN. The authors prove that as m→∞, the corresponding solutions um(t)→u_=f+Δw in L1(RN), uniformly for t in a compact set in ]0,∞[, where 0≤w_∈L1(Rn) is the solution of the variational inequality Δw_∈L1(RN), 0≤f+Δw_≤1, w_(f+Δw_ −1)=0 a.e. The authors also show similar results for the same equation on a bounded open set Ω in RN with Dirichlet or Neumann boundary conditions
PB Libreria Editrice Universitaria Levrotto & Bella
SN 0373-1243
YR 1989
FD 1989
LK https://hdl.handle.net/20.500.14352/60767
UL https://hdl.handle.net/20.500.14352/60767
LA eng
NO D.G. Aronson, Ph. Bénilan. Régularité des solutions de l'équations des milieux poreux dans  RN. C.R.Ac. Se. Paris 288 (1979), pp. 103-105. Ph. Bénilan, A strong regularity Lp for solutions of the porous medium equation. Contribution nonlinear pde. Res. Notes in Math. 89. Pitman (1983), pp. 39-58. Ph. Bénilan, H. Brézis, M.G. Crandall. A semilinear elliptic equation in L1(RN). Ann. Sc. Norm. Sup. Pisa. V,2. (1975), pp. 523-555. Ph. Bénilan, M.G. Crandall. Regularizing effect of homogeneous evolutions equations. Contributions to Analysis and Geometry, D.N. Clarke & al eds, John Hopkins Un. Press, Baltimore (1981), pp. 23-30. Ph. Bénilan, M.G. Crandall, P.E. Sacks. Some L1 existence and dependance results for semilinear elliptic equations under nonlinear boundary conditions. Appl. Math. Optim. 17 (1988), pp. 203-224. H. Brézis, W. Strauss. Semilinear elliptic equations in L1. J. Math. Soc. Japan, 25 (1973), pp. 565-590.L.A. Caffarelli, A. Friedman. Asymptotic behavior of solutions of ut = Δum as m → ∞. Indiana Un. Math. J. 36,4 (1987), pp. 711-718. C.M. Elliot, M.A. Herrero, J.R. King. J.R. Ockendon. The mesa problem: diffusion patterns for ut = (umu) as m → ∞. IMA J. Appl. Maths 37 (1986), pp. 147-154. P.E. Sacks. A gingillar limit problem for the porous medium equation. J.Math. Anal. Appl. 140,2 (1989), pp. 456-466.
NO Proceedings of the conference held in Turin, October 2–6, 1989
DS Docta Complutense
RD 6 may 2024