In this paper we prove existence of nonnegative solutions to parabolic Cauchy–Dirichlet problems with (eventually) singular superlinear gradient terms. The model equation is ut-Δpu=g(u)|∇u|q+h(u)f(t,x)in(0,T)×Ω,where Ω is an open bounded subset of RN with N> 2 , 0 < T< + ∞, 1 < p< N, and q< p is superlinear. The functions g,h are continuous and possibly satisfying g(0) = + ∞ and/or h(0) = + ∞, with different rates. Finally, f is nonnegative and it belongs to a suitable Lebesgue space. We investigate the relation among the superlinear threshold of q, the regularity of the initial datum and the forcing term, and the decay rates of g,h at infinity.

On some parabolic equations involving superlinear singular gradient terms / Magliocca, Martina; Oliva, Francescantonio. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 21:2(2021), pp. 2547-2590. [10.1007/s00028-021-00695-1]

On some parabolic equations involving superlinear singular gradient terms

Martina Magliocca;Francescantonio Oliva
2021

Abstract

In this paper we prove existence of nonnegative solutions to parabolic Cauchy–Dirichlet problems with (eventually) singular superlinear gradient terms. The model equation is ut-Δpu=g(u)|∇u|q+h(u)f(t,x)in(0,T)×Ω,where Ω is an open bounded subset of RN with N> 2 , 0 < T< + ∞, 1 < p< N, and q< p is superlinear. The functions g,h are continuous and possibly satisfying g(0) = + ∞ and/or h(0) = + ∞, with different rates. Finally, f is nonnegative and it belongs to a suitable Lebesgue space. We investigate the relation among the superlinear threshold of q, the regularity of the initial datum and the forcing term, and the decay rates of g,h at infinity.
2021
Nonlinear parabolic equations; Repulsive Gradient; Singular parabolic equations
01 Pubblicazione su rivista::01a Articolo in rivista
On some parabolic equations involving superlinear singular gradient terms / Magliocca, Martina; Oliva, Francescantonio. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 21:2(2021), pp. 2547-2590. [10.1007/s00028-021-00695-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1674505
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