Complete blow up and global behaviour of solutions of \(u_t- \Delta u=g(u)\)

DOI10.1016/S0294-1449(99)80002-XzbMath0914.35057MaRDI QIDQ1276062

Yvan Martel

Publication date: 14 June 1999

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1998__15_6_687_0

zbMATH Keywords

nonlinear heat equationconvergence rateblow up in infinite time

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (17)

COMPLETE BLOW-UP AND THERMAL AVALANCHE FOR HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS ⋮ Complete blow-up and incomplete quenching for the heat equation with a nonlinear boundary condition ⋮ Existence and stability of equilibrium solutions of a nonlinear heat equation ⋮ Recent results on blow-up and quenching for nonlinear Volterra equations ⋮ Multiple blow-up for a porous medium equation with reaction ⋮ On nonexistence of Baras-Goldstein type without positivity assumptions for singular linear and nonlinear parabolic equations ⋮ Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient ⋮ A priori bounds and complete blow up of positive solutions of indefinite superlinear parabolic problems ⋮ Optimal regularity conditions for elliptic problems via \(L^p_\delta\)-spaces ⋮ Recent Mathematical Results on Combustion in Hydraulically Resistant Porous Media ⋮ Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions ⋮ Existence and nonexistence of positive solutions to a fractional parabolic problem with singular weight at the boundary ⋮ Thermal avalanche for blowup solutions of semilinear heat equations ⋮ Extremal solutions to Liouville–Gelfand type elliptic problems with nonlinear Neumann boundary conditions ⋮ Thermal avalanche after non-simultaneous blow-up in heat equations coupled via nonlinear boundary ⋮ On the KPZ equation with fractional diffusion: global regularity and existence results ⋮ A semilinear parabolic problem with singular term at the boundary

Cites Work

• Unnamed Item
• On the asymptotic behavior of solutions of certain quasilinear parabolic equations
• Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
• Complete blow-up after \(T_{\max}\) for the solution of a semilinear heat equation
• Global, unbounded solutions to a parabolic equation
• Blow up for \(u_ t- \Delta u=g(u)\) revisited
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions
• The study of a bifurcation problem associated to an asymptotically linear function
• On the nonlinear equations Δ𝑢+𝑒^{𝑢}=0 and ∂𝑣/∂𝑡=Δ𝑣+𝑒^{𝑣}

This page was built for publication: Complete blow up and global behaviour of solutions of \(u_t- \Delta u=g(u)\)