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Regularizing effects for \(u_ t\) + A phi(u) = 0 in \(L^ 1\). (English) Zbl 0483.35076


MSC:

35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
35B45 A priori estimates in context of PDEs
47H05 Monotone operators and generalizations
58D25 Equations in function spaces; evolution equations
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[1] Aronson, D. G.; Bénilan, Ph, Régularité des solutions de l’équation des milieux poreux dans \(R^N\), C. R. Acad. Sci. Paris Ser. A-B, 288, 103-105 (1979) · Zbl 0397.35034
[2] Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces (1976), Noordhoff: Noordhoff Leyden
[3] Bénilan, Ph; Brézis, H.; Crandall, M. G., A semilinear elliptic equation in \(L^1(R^N)\), Ann. Scuola Norm. Sup. Pisa Cl. Sci (4), 2, 523-555 (1975) · Zbl 0314.35077
[4] Ph. Bénilan and M. G. CrandallAmer. J. Math.; Ph. Bénilan and M. G. CrandallAmer. J. Math.
[5] Brézis, H.; Strauss, W., Semilinear elliptic equations in \(L^1\), J. Math. Soc. Japan, 25, 15-26 (1973)
[6] Crandall, M. G., An introduction to evolution governed by accretive operators, (Cesari, L.; Hale, J.; LaSalle, J., Dynamical Systems-An International Symposium (1976), Academic Press: Academic Press New York), 131-165
[7] Crandall, M. G.; Pazy, A.; Tartar, L., Remarks on generators of analytic semigroups, Israel J. Math., 32, 363-374 (1979) · Zbl 0436.47028
[8] M. G. Crandall and M. Pierre\(u_t Δϑ u\)Trans. Amer. Math. Soc.; M. G. Crandall and M. Pierre\(u_t Δϑ u\)Trans. Amer. Math. Soc.
[9] Evans, L. C., Application of nonlinear semigroup theory to certain partial differential equations, (Crandall, M. G., Nonlinear Evolution Equations (1978), Academic Press: Academic Press New York) · Zbl 0471.35039
[10] Lê, C.-H, Étude de la classe des opérateurs \(m\)-accrétifs de \(L^1(Ω)\) et accrétifs dans \(L^∞(Ω), 3\) rd cycle thesis (1977), Paris VI
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