Critical nonlinearities in partial differential equations

DOI10.1007/s00032-009-0106-7zbMath1205.35024OpenAlexW2045254662MaRDI QIDQ5894135

Pohozaev, Stanislav I.

Publication date: 19 February 2011

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-009-0106-7

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Critical exponents in context of PDEs (35B33) Blow-up in context of PDEs (35B44)

Related Items (15)

Blow-up of solutions of some nonlinear inequalities in unbounded domains ⋮ Blow-up of the solution of a nonlinear system of equations with positive energy ⋮ Blow-up of positive-energy solutions of a dissipative system in classical field theory ⋮ Blowup of solutions of the three-dimensional Rosenau-Burgers equation ⋮ Blowup of a positive-energy solution of model wave equations in nonlinear dynamics ⋮ Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds ⋮ On the blow-up of solutions of the Benjamin-Bona-Mahony-Burgers and Rosenau-Burgers equations ⋮ On the blow-up of the solution of an equation related to the Hamilton-Jacobi equation ⋮ A note on Liouville type theorem of elliptic inequality \(\delta u+u^\sigma\leqslant 0\) on Riemannian manifolds ⋮ Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein-Gordon equations in the de Sitter metric ⋮ On the blow-up of the solution of an equation with a gradient nonlinearity ⋮ On blowup of solutions to a Kirchhoff type dissipative wave equation with a source and positive energy ⋮ Blow-up of solutions of strongly dissipative generalized Klein-Gordon equations ⋮ Solution blow-up in a nonlinear system of equations with positive energy in field theory ⋮ On Nonnegative Solutions of the Inequality Δ u + u^σ ≤ 0 on Riemannian Manifolds

Cites Work

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• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
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