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March  2006, 5(1): 155-179. doi: 10.3934/cpaa.2006.5.155

Nonuniqueness of solutions to semilinear parabolic equations with singular coefficients

 1 Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza” P.le A. Moro 5, I-00185, Roma, Italy 2 Depto. de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés 28911, Madrid, Spain 3 Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", P.le A. Moro 5, I-00185 Roma

Received  March 2005 Revised  September 2005 Published  December 2005

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.
Citation: Luisa Moschini, Guillermo Reyes, Alberto Tesei. Nonuniqueness of solutions to semilinear parabolic equations with singular coefficients. Communications on Pure & Applied Analysis, 2006, 5 (1) : 155-179. doi: 10.3934/cpaa.2006.5.155
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