Some noncoercive parabolic equations with lower order termsin divergence form |
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| Authors: | Lucio?Boccardo mailto:none" title=" none" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Luigi?Orsina,Alessio?Porretta |
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| Affiliation: | (1) Dipartimento di Matematica, Università di Roma 1, Piazza A. Moro 2, 00185 Roma, Italy;(2) Dipartimento di Matematica, Università di Roma "La Sapienza", Piazza le A. Moro 2, 00185 Roma, Italy;(3) Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy |
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| Abstract: | ![]()
This paper deals with existence and regularity results for the problem$ cases{u_t-mathrm{div}(a(x,t,u )nabla u)=-mathrm{div}(u,E)qquad in Omegatimes (0,T),cr u=0 qquad on partial Omegatimes (0,T), cr u (0)= u_0 qquad in Omega ,cr} $under various assumptions on E and $ u_0 $. The main difculty in studying this problem is due to the presence of theterm div(uE), which makes the differential operator non coercive on the "energy space" $ L^2 (0, T; H_0^1 (Omega)) $.AMS Subject Classification: 35K10, 35K15, 35K65. |
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| Keywords: | Nonlinear parabolic equations noncoercive problems infinite energy solutions |
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