Simondon, Frédérique Strong solutions for \(u_ t=\phi (u)_{xx}-f(t)\psi (u)_ x\). (English) Zbl 0665.35038 Commun. Partial Differ. Equations 13, No. 11, 1337-1354 (1988). Consider the nonlinear parabolic equation \[ (1)\quad u_ t=\phi (u)_{xx}-f(t)\psi (u)_ x\quad on\quad \Omega \subset (0,\infty)\times {\mathbb{R}}. \] This paper establishes a local result for the regularity of generalized solutions for the problem with one or two degeneracies and proves that, under certain conditions all the derivatives involved are functions and the equation (1) is satisfied almost everywhere. Reviewer: J.H.Tian Cited in 4 Documents MSC: 35K55 Nonlinear parabolic equations 35B60 Continuation and prolongation of solutions to PDEs 35D10 Regularity of generalized solutions of PDE (MSC2000) Keywords:strong solutions; nonlinear parabolic equation; regularity; generalized solutions PDFBibTeX XMLCite \textit{F. Simondon}, Commun. Partial Differ. Equations 13, No. 11, 1337--1354 (1988; Zbl 0665.35038) Full Text: DOI References: [1] Bénilan, P. 1981. Evolution equations and accretive operators. Lect. Notes, University of Kentucky. 1981. [2] P. Bénilan, A strong regularity Lp for solutions of the porous media equation, Research notes in mathematics, no 89, Contribution to nonlinear differential equations, c. Bardos ed. Pitman [3] P. Bénilan, Notes personnelles [4] Bénilan P., Indiana University Mathematics Journal 33 (1) (1984) · Zbl 0552.35045 · doi:10.1512/iumj.1984.33.33003 [5] Chavent, G. 1979. Mathematical modelling of mono and diphasic oil or gas reservoirs. Lecture notes of a course. July1979, Petroperu. [6] Crandall M.G., J. Funct. Anal 45 pp 194– (1982) · Zbl 0483.35076 · doi:10.1016/0022-1236(82)90018-0 [7] Diaz J.I., University of Wiscons in-Madison, Mathematics Research Center Technical Summer Report 2502 pp 40– (1983) [8] Friedman A., Prentice Hall, Englewood Cliffs, N.J (1964) [9] Gagneux, G. ”Thèse de Doctoral d’état”. Université de Besan{\(\varsigma\)}on. [10] Gilding B.H., J. London Math. Soc 13 (2) pp 103– (1976) · Zbl 0319.35045 · doi:10.1112/jlms/s2-13.1.103 [11] Gilding B.H., Technische Hogeschool Twente Memorandum (1986) [12] Gilding B.H., Arch.Rational Mech. Anal 61 pp 127– (1976) · Zbl 0336.76037 · doi:10.1007/BF00249701 [13] Ladyzenskaja O.A., Translations of Mathematical Monographs 23 (1968) [14] Simondon, F. ”Thè”. Université de Besan{\(\varsigma\)}on. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.