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Linear diffusion with singular absorption potential and/or unbounded convective flow: the weighted space approach

Abstract:

In this paper we prove the existence and uniqueness of very weak solutions to linear diffusion equations involving a singular absorption potential and/or an unbounded convective flow on a bounded open set of IRN. In most of the paper we consider homogeneous Dirichlet boundary conditions but we prove that when the potential function grows faster than the distance to the boundary to the power -2 then no boundary condition is required to get the uniqueness of very weak solutions. This result is ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.3934/dcds.2018023

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0001-8360-3250
Publisher:
American Institute of Mathematical Sciences
Journal:
Discrete and Continuous Dynamical Systems More from this journal
Volume:
38
Issue:
2
Pages:
509-546
Publication date:
2018-02-01
Acceptance date:
2018-02-01
DOI:
EISSN:
1553-5231
ISSN:
1078-0947

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