We prove nonuniqueness of solutions of the Cauchy problem for a semilinear parabolic equation with inverse-square potential in certain Lebesgue spaces. The nonuniqueness results proved in [5] are the limiting case of the present ones as the strength of the potential vanishes. Similar results are obtained for a related semilinear parabolic equation with singular coefficients. The proofs rely on investigating by variational methods in suitable weighted Sobolev spaces the equation satisfied by the profile of a radial similarity solution.
NONUNIQUENESS OF SOLUTIONS TO A SEMILINEAR PARABOLIC EQUATION WITH SINGULAR COEFFICIENTS / Moschini, Luisa; Reyes, G.; Tesei, Alberto. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 5:(2006), pp. 155-179. [10.3934/cpaa.2006.5.155]
NONUNIQUENESS OF SOLUTIONS TO A SEMILINEAR PARABOLIC EQUATION WITH SINGULAR COEFFICIENTS
MOSCHINI, Luisa;TESEI, Alberto
2006
Abstract
We prove nonuniqueness of solutions of the Cauchy problem for a semilinear parabolic equation with inverse-square potential in certain Lebesgue spaces. The nonuniqueness results proved in [5] are the limiting case of the present ones as the strength of the potential vanishes. Similar results are obtained for a related semilinear parabolic equation with singular coefficients. The proofs rely on investigating by variational methods in suitable weighted Sobolev spaces the equation satisfied by the profile of a radial similarity solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
