Artículo
Regularity for degenerate evolution equations with strong absorption
Fecha de publicación:
06/2018
Editorial:
Academic Press Inc Elsevier Science
Revista:
Journal Of Differential Equations
ISSN:
0022-0396
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of p-Laplacian type (2 ≤ p < ∞) under a strong absorption condition: Δpu − ∂u/∂t = λ0uq + in ΩT := Ω × (0,T), where 0 ≤ q < 1. This model is interesting because it yields the formation of dead-core sets, i.e., regions where non-negative solutions vanish identically. We shall prove sharp and improved parabolic Cα regularity estimates along the set F0(u, ΩT) = ∂{u > 0} ∩ΩT (the free boundary), where α = p/p−1−q ≥ 1 + 1/p−1. Some weak geometric and measure theoretical properties as non-degeneracy, positive density, porosity and finite speed of propagation are proved. As an application, we prove a Liouville-type result for entire solutions. A specific analysis for Blow-up type solutions will be done as well. The results are new even for dead-core problems driven by the heat operator.
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Articulos(CCT - MENDOZA)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - MENDOZA
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - MENDOZA
Articulos(IMASL)
Articulos de INST. DE MATEMATICA APLICADA DE SAN LUIS
Articulos de INST. DE MATEMATICA APLICADA DE SAN LUIS
Articulos(OCA CIUDAD UNIVERSITARIA)
Articulos de OFICINA DE COORDINACION ADMINISTRATIVA CIUDAD UNIVERSITARIA
Articulos de OFICINA DE COORDINACION ADMINISTRATIVA CIUDAD UNIVERSITARIA
Citación
Da Silva, Joao Vitor; Ochoa, Pablo Daniel; Silva, Analia; Regularity for degenerate evolution equations with strong absorption; Academic Press Inc Elsevier Science; Journal Of Differential Equations; 264; 12; 6-2018; 7270-7293
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