×

zbMATH — the first resource for mathematics

Problèmes paraboliques semilinéaires avec données mesures. (Semilinear parabolic problems with given measures). (French) Zbl 0582.35060
The authors study semilinear evolution equations of the form \[ (*)\quad \partial u/\partial t-\Delta u+u| u|^{\gamma -1}=f\quad in\quad (0,T)\times \Omega;\quad u(0)=\nu \quad in\quad \Omega \] (f and \(\nu\) are given measures). They prove that (*) has a solution if and only if f and \(\nu\) are not too ”concentrated” and do not charge too thin sets. Further they solve the question of removability of singularities for (*) completely.

MSC:
35K55 Nonlinear parabolic equations
31C10 Pluriharmonic and plurisubharmonic functions
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brezis, H. and Friedman, A. 1982. ”MRC Report 2277”. Wisconsin, U.S.A: Un of Madison.
[2] Baras, P. and Pierre, M. 1984.Ann. Tnst. Fourier, Vol. 295, 519–522. Paris, Grenoble: C.R. A. S.
[3] Meyers N.G., Math.scand 26 pp 255– (1970)
[4] Adams D.R., Indiana lrn. J. 22 (9) pp 873– (1971) · Zbl 0285.31007
[5] Ladyzenskaja O.A., Linear and quasi1i.near equations of parabolic type 23 (1968)
[6] Solonnikov, V.A. 1967.Trudy Math. Inst.Steklov, 65 Vol. 70, 133–51. A.M.S. Providence.
[7] Adams D.R., Ark Mat 14 pp 125– (1976) · Zbl 0325.31008
[8] Besov O.V., A.M.S. Trans 1 40 (2) pp 85– (1964)
[9] Lions, J.L. and Peetre, J. 1964.Stir tine cJasse d1 espaces df interpolation, Vol. 19, 5–68. I.H.E.S: Publ. Math. n.
[10] Aronszajn N., Ann. lust. Fourier 13 (2) pp 211– (1963) · Zbl 0121.09604
[11] Stein E.M., Bull A.M.S 68 (2) pp 577– (1962)
[12] Rogers O.A., Hausdorff measures (1970)
[13] Kates T., Israel J. Math 13 pp 135– (1972) · Zbl 0246.35025
[14] Grun-Rehomme M., J. Math. Pures et Appli 56 pp 149– (1977)
[15] Nirenberg L., Ann. Scuola Norm.Sup. Pisa 13 pp 115– (1959)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.