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Global and blow up solutions for a semilinear heat equation with variable reaction reaction on a general domain
  • Miguel Loayza,
  • Ricardo Castillo
Miguel Loayza
Universidade Federal de Pernambuco

Corresponding Author:[email protected]

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Ricardo Castillo
Universidad del Bio Bio Facultad de Ciencias
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We are concerned with the existence of global and blow-up solutions for the semilinear heat equation with variable exponent u t - Δ u = h ( t ) f ( u ) p ( x ) in Ω×(0 ,T) with zero Dirichlet boundary condition and initial data in C 0 ( Ω ) . The scope of our analysis encompasses both bounded and unbounded domains, with p ( x ) ∈ C ( Ω ) , 0 < p - ≤ p ( x ) ≤ p + , hC(0 ,∞), and fC[0 ,∞). Our findings have significant implications, as they enhance the blow-up result discovered by Castillo and Loayza in Comput. Math. App. 74(3), 351-359 (2017) when f( u)= u.
18 Jul 2023Submitted to Mathematical Methods in the Applied Sciences
18 Jul 2023Assigned to Editor
18 Jul 2023Submission Checks Completed
26 Jul 2023Review(s) Completed, Editorial Evaluation Pending
03 Aug 2023Reviewer(s) Assigned