Weak Periodic Solution for Semilinear Parabolic Problem with Singular Nonlinearities and L1 Data

We consider a periodic parabolic problem involving singular nonlinearity and homogeneous Dirichlet boundary condition modeled by ∂ u ∂ t - Δ u = f u γ in Q T , where T > 0 is a period, Ω is an open regular bounded subset of R N , Q T = ] 0 , T [ × Ω , γ ∈ R and f is a nonnegative integrable funct...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2020, Vol.17 (4)
Main Authors: Charkaoui, Abderrahim, Alaa, Nour Eddine
Format: Article
Language:English
Subjects:
Boundary conditions
Dirichlet problem
Mathematical functions
Mathematics
Mathematics and Statistics
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Summary:We consider a periodic parabolic problem involving singular nonlinearity and homogeneous Dirichlet boundary condition modeled by ∂ u ∂ t - Δ u = f u γ in Q T , where T > 0 is a period, Ω is an open regular bounded subset of R N , Q T = ] 0 , T [ × Ω , γ ∈ R and f is a nonnegative integrable function periodic in time with period T . Under a suitable assumptions on f , we establish the existence of a weak T-periodic solution for all ranges of value of γ .
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-020-01535-1