Optimal Liouville-type theorems for a system of parabolic inequalities

DOI10.1142/S0219199719500433zbMath1445.35097WikidataQ128000313 ScholiaQ128000313MaRDI QIDQ5117124

Quoc Hung Phan, Anh Tuan Duong

Publication date: 20 August 2020

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

parabolic systemLiouville-type theoremparabolic inequalityFujita result

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Critical exponents in context of PDEs (35B33) Partial differential inequalities and systems of partial differential inequalities (35R45) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items

Optimal Liouville type theorems for porous medium systems with sources ⋮ Fujita type results for a quasilinear parabolic inequality of Hardy-Hénon type with time forcing terms ⋮ On positive supersolutions of fractional elliptic equations with gradient terms ⋮ Liouville type theorems for fractional parabolic problems ⋮ Liouville-type theorem for one-dimensional porous medium systems with sources ⋮ Liouville type theorems for degenerate parabolic systems with advection terms ⋮ A note on positive supersolutions of the fractional Lane-Emden system ⋮ Fujita type results for quasilinear parabolic inequalities with nonlocal terms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Hardy-Littlewood-Sobolev type systems
• A new dynamical approach of Emden-Fowler equations and systems
• Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
• Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
• Liouville theorems, universal estimates and periodic solutions for cooperative parabolic Lotka-Volterra systems
• The proof of the Lane-Emden conjecture in four space dimensions
• Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
• Boundedness and blow up for a semilinear reaction-diffusion system
• Liouville theorems and blow up behaviour in semilinear reaction diffusion systems
• A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems
• Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
• Non-existence of positive solutions of Lane-Emden systems
• Non-existence results for semilinear cooperative elliptic systems via moving spheres
• A Liouville comparison principle for solutions of quasilinear singular parabolic inequalities
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
• A Liouville comparison principle for solutions of semilinear parabolic inequalities in the whole space
• A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation
• Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure
• Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems
• Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle
• Blow-up of solutions of nonlinear parabolic inequalities
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part II: Parabolic equations