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Existence results for some anisotropic degenerate parabolic problems with lower-order term and source
Resultados de existencia para algunos problemas parabólicos degenerados anisotrópicos con términos y funciones de fuente de orden inferior
DOI:
https://doi.org/10.15446/recolma.v59n2.125946Palabras clave:
L∞ estimates, nonlinear anisotropic parabolic equations, degenerate coercivity (en)Estimados L∞, ecuaciones anisotrópicas parabólicas no lineales, coercitividad degenerada (es)
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In this study, we establish the existence and regularity of weak solutions for the anisotropic degenerate parabolic equation, namely.
∂tu − ΣNi=1 (Di(ai(t, x, u)|Di u|pi−2 Di u) + |u|τpi−2 u|Di u|pi ) = |u|r−2 u,
if 1 ≤ r < τp− + 1 and τ ≥ 1/p− with p− = min1 ≤ i ≤ N pi, then there exists a non-negative weak solution for every positive initial data in L1.
En este artículo, probamos la existencia y regularidad de las soluciones de la ecuación parabólica anisotrópica no lineal
∂tu − ΣNi=1 (Di(ai(t, x, u)|Di u|pi−2 Di u) + |u|τpi−2 u|Di u|pi ) = |u|r−2 u,
si 1 ≤ r < τp− + 1 y τ ≥ 1/p− con p− = min1 ≤ i ≤ N pi. Probamos la existencia de una solución débil cuando los datos iniciales son funciones en L1.
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