Self-similar solutions of a semilinear parabolic equation with inverse-square potential
Journal of Differential Equations, ISSN: 0022-0396, Vol: 219, Issue: 1, Page: 40-77
2005
- 4Citations
- 3Captures
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Article Description
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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0022039605002366; http://dx.doi.org/10.1016/j.jde.2005.06.031; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=27944436203&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0022039605002366; https://dx.doi.org/10.1016/j.jde.2005.06.031
Elsevier BV
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