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• W4312925614 abstract "We consider the porous medium equation subject to zero-Dirichlet conditions on a variety of two-dimensional domains, namely strips, slender domains and sectors, allowing us to capture a number of different classes of behaviours. Our focus is on intermediate-asymptotic descriptions, derived by formal arguments and validated against numerical computations. While our emphasis is on non-negative solutions to the slow-diffusion case, we also derive a number of results for sign-change solutions and for fast diffusion. Self-similar solutions of various kinds play a central role, alongside the identification of suitable conserved quantities. The characterisation of domains exhibiting infinite-time hole closure is a particular upshot and we highlight a number of open problems." @default.
• W4312925614 created "2023-01-05" @default.
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• W4312925614 date "2023-01-01" @default.
• W4312925614 modified "2023-10-10" @default.
• W4312925614 title "Cauchy-Dirichlet problems for the porous medium equation" @default.
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• W4312925614 doi "https://doi.org/10.3934/dcds.2022182" @default.
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