On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 3, pp. 363-441.
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     author = {Andreucci, D. and Di Benedetto, E.},
     title = {On the {Cauchy} problem and initial traces for a class of evolution equations with strongly nonlinear sources},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {363--441},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 18},
     number = {3},
     year = {1991},
     mrnumber = {1145316},
     zbl = {0762.35052},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1991_4_18_3_363_0/}
}
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Andreucci, D.; Di Benedetto, E. On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 3, pp. 363-441. http://www.numdam.org/item/ASNSP_1991_4_18_3_363_0/

[1] D. Andreucci, L∞-estimates for local solutions of degenerate parabolic equations, to appear on S.I.A.M. J. Math. Anal.. | Zbl

[2] D. Andreucci - E. Di Benedetto, A new approach to initial traces in nonlinear filtration, to appear on Ann. Inst. H. Poincaré Anal. Non Linéaire. | Numdam | MR | Zbl

[3] C. Bandle - H.A. Levine, On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains, Trans. Amer. Math. Soc., 316 (1989), pp. 595-622. | MR | Zbl

[4] P. Baras, Non-unicité des solutions d'une équation d'évolution non-linéaire, Ann. Fac. Sci. Toulouse Math., 5 (1983), pp. 287-302. | Numdam | MR | Zbl

[5] P. Baras - R. Kersner, Local and global solvability of a class of semilinear parabolic equations, J. Differential Equations, 68 (1987), pp. 238-252. | MR | Zbl

[6] P. Baras - M. Pierre, Problems paraboliques semi-linéaires avec donnees measures, Appl. Anal., 18 (1984), pp. 111-149. | MR | Zbl

[7] P. Baras - M. Pierre, Critère d'existence de solutions positives pour des équations semi-linéaires non monotones, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), pp. 185-212. | Numdam | MR | Zbl

[8] G.I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh., 16 (1952), pp. 67-78. | MR | Zbl

[9] Ph. Bènilan - M.G. Crandall - M. Pierre, Solutions of the porous medium equation in RN under optimal conditions on initial values, Indiana Univ. Math. J., 33 (1984), pp. 51-87. | MR | Zbl

[10] H. Brézis - A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl., 62 (1983), pp. 73-97. | MR | Zbl

[11] E. Di Benedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J., 32 (1983), pp. 83-118. | MR | Zbl

[12] E. Di Benedetto - M.A. Herrero, On the Cauchy problem and initial traces for a degenerate parabolic equation, Trans. Amer. Math. Soc., 314 (1989), pp. 187-224. | MR | Zbl

[13] H. Fujita, On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 13 (1966), pp. 109-124. | Zbl

[14] V.A. Galaktionov, The conditions for there to be no global solutions of a class of quasi-linear parabolic equations, Zh. Vychisl. Mat. i Mat. Fiz., 22 (2) (1982), pp. 322-338; Engl. Transl. U.S.S.R. Comput. Math. and Math. Phys., 22 (2) (1982), pp. 73-90. | MR | Zbl

[15] V.A. Galaktionov, The existence and non-existence of global solutions of boundary value problems for quasi-linear parabolic equations, Zh. Vychisl. Mat. i Mat. Fiz., 22 (6) (1982), pp. 1369-1385; Engl. Transl. U.S.S.R. Comput. Math. and Math. Phys., 22 (6) (1982), pp. 88-107. | MR | Zbl

[16] V.A. Galaktionov - S.P. Kurdyumov - A.P. Mikhailov - A.A. Samarskji, Unbounded solutions of the Cauchy problem for the parabolic equation ut=∇(uσ ∇u)+uβ, Dokl. Akad. Nauk SSSR, 252 (1980), pp. 1362-1364; Engl. Transl. Soviet Phys. Dokl., 25 (1980), pp. 458-459. | Zbl

[17] V.A. Galaktionov, S.A. Posashkov, Estimates of localized unbounded solutions of quasilinear parabolic equations, Differentsial'nye Uravneniya, 23 (1987), pp. 1133-1143; Engl. Transl. Differential Equations, 23 (1987), pp. 750-759. | MR | Zbl

[18] Y. Giga, R.V. Kohn, Characterizing blow-up using similarity variables, Indiana Univ. Math. J., 36 (1987), pp. 3-40. | MR | Zbl

[19] A. Haraux - F.B. Weissler, Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J., 31 (1982), pp. 167-189. | MR | Zbl

[20] A.S. Kalashnikov, On a heat conduction equation for a medium with non-uniformly distributed non-linear heat sources or absorbers, Moscow Univ., Math. Mech. Bull., 3 (1983), pp. 20-24. | MR | Zbl

[21] S. Kamin - Ph. Rosenau, Non-linear diffusion in a finite mass medium, Comm. Pure Appl. Math., 35 (1982), pp. 113-127. | MR | Zbl

[22] S. Kamin - PH. ROSENAU, Non-linear thermal evolution in an inhomogeneous medium, J. Math. Phys., 23 (1982), pp. 1385-1390. | MR | Zbl

[23] J. Kaplan, On the growth of solutions of quasi-linear parabolic equations, Comm. Pure Appl. Math., 16 (1963), pp. 305-330. | MR | Zbl

[24] O. Kavian, Remarks on the large time behaviour of a nonlinear diffusion equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 4 (1987), pp. 423-452. | Numdam | MR | Zbl

[25] H.A. Levine - P. Meier, The value of the critical exponent for reaction-diffusion equations in cones, Arch. Rational Mech. Anal., 109 (1990), pp. 73-80. | MR | Zbl

[26] H.A. Levine - P.E. Sacks, Some existence and nonexistence theorems for solutions of degenerate parabolic equations, J. Differential Equations, 52 (1984), pp. 135-161. | MR | Zbl

[27] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'Tzeva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs. 23 AMS, Providence, R.I. (1968). | Zbl

[28] P. Meier, On the critical exponent for reaction-diffusion equations, Arch. Rational Mech. Anal., 109 (1990), pp. 63-71. | MR | Zbl

[29] N.G. Meyers, A theory of capacities for potentials of functions in Lebesgue classes, Math. Scand., 26 (1970), pp. 255-292. | MR | Zbl

[30] G. Minty, Monotone (non-linear) operators in Hilbert spaces, Duke Math. J., 29 (1962), pp. 341-346. | MR | Zbl

[31] R.E. Pattle, Diffusion from an instantaneous point source with a concentration dependent coefficient, Quart. Appl. Math., 12 (1959), pp. 407-409. | MR | Zbl

[32] P.E. Sacks, The initial and boundary value problem for a class of degenerate parabolic equations, Comm. Partial Differential Equations, 8 (1983), pp. 693-733. | MR | Zbl

[33] F.B. Weissler, Local existence and nonexistence for semilinear parabolic equations in Lp, Indiana Univ. Math. J., 29 (1980), pp. 79-102. | MR | Zbl

[34] F.B. Weissler, Existence and non-existence of global solutions for a semilinear heat equation, Israel J. Math., 38 (1981), pp. 29-40. | MR | Zbl