Unbounded solutions of the nonlocal heat equation Articles uri icon

publication date

  • November 2011

start page

  • 1663

end page

  • 1686


  • 6


  • 10

International Standard Serial Number (ISSN)

  • 1534-0392

Electronic International Standard Serial Number (EISSN)

  • 1553-5258


  • We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation ut=Jastu-ui: where J is a symmetric continuous probability density. Depending on the tail of J, we give a rather complete picture of the problem in optimal classes of data by (i): estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a suitable class; (iii) proving blow-up in finite time in the case of some critical growths; (iv) giving explicit unbounded polynomial solutions.