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• W3136145246 abstract "Abstract We consider the porous medium equation with a power-like reaction term, posed on Riemannian manifolds. Under certain assumptions on p and m in (1.1), and for small enough nonnegative initial data, we prove existence of global in time solutions, provided that the Sobolev inequality holds on the manifold. Furthermore, when both the Sobolev and the Poincaré inequalities hold, similar results hold under weaker assumptions on the forcing term. By the same functional analytic methods, we investigate global existence for solutions to the porous medium equation with source term and variable density in $${{mathbb {R}}}^n$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> ." @default.
• W3136145246 created "2021-03-29" @default.
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• W3136145246 date "2021-03-24" @default.
• W3136145246 modified "2023-10-14" @default.
• W3136145246 title "Global existence of solutions and smoothing effects for classes of reaction–diffusion equations on manifolds" @default.
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• W3136145246 doi "https://doi.org/10.1007/s00028-021-00685-3" @default.
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