We investigate existence, nonexistence and asymptotical behaviour-both at the origin and at infinity-of radial self-similar solutions to a semilinear parabolic equation with inverse-square potential. These solutions are relevant to prove nonuniqueness of the Cauchy problem for the parabolic equation in certain Lebesgue spaces, generalizing the result proved by Haraux and Weissler [Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J. 31 (1982) 167-189] for the case of vanishing potential. (c) 2005 Elsevier Inc. All rights reserved.
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机译：我们研究具有反平方势的半线性抛物方程的原点和无穷大的径向自相似解的存在性，不存在性和渐近行为。这些解决方案与证明在某些Lebesgue空间中抛物方程的柯西问题的非唯一性有关，并推广了Haraux和Weissler证明的结果[半线性初值问题的非唯一性，印第安纳大学。数学。 J. 31（1982）167-189]。 （c）2005 Elsevier Inc.保留所有权利。
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