We study well-posedness of initial value problems for a class of singular quasilinear parabolic equations in one space dimension. Simple conditions for well-posedness in the space of bounded nonnegative solutions are given, which involve boundedness of solutions of some related linear stationary problems. By a suitable change of unknown, the above results can be applied to classical initial-boundary value problems for parabolic equations with singular coefficients, as the heat equation with inverse square potential. (C) 2003 Elsevier Inc. All rights reserved.
Well-posedness of initial value problems for singular parabolic equations / Robert, Kersner; Tesei, Alberto. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 199:1(2004), pp. 47-76. [10.1016/j.jde.2003.10.015]
Well-posedness of initial value problems for singular parabolic equations
TESEI, Alberto
2004
Abstract
We study well-posedness of initial value problems for a class of singular quasilinear parabolic equations in one space dimension. Simple conditions for well-posedness in the space of bounded nonnegative solutions are given, which involve boundedness of solutions of some related linear stationary problems. By a suitable change of unknown, the above results can be applied to classical initial-boundary value problems for parabolic equations with singular coefficients, as the heat equation with inverse square potential. (C) 2003 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
