Stability of stationary solutions for semilinear heat equations with concave nonlinearity

DOI10.1142/S0219199715500017zbMath1334.35143MaRDI QIDQ3465802

Goro Akagi, Ryuji Kajikiya

Publication date: 22 January 2016

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

zbMATH Keywords

stabilityasymptotic behavioreigenvalue problemlinearized problemsublinear heat equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Semilinear parabolic equations (35K58)

Related Items (3)

Stability and instability of stationary solutions for sublinear parabolic equations ⋮ Linearized stability for degenerate and singular semilinear and quasilinear parabolic problems: the linearized singular equation ⋮ Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for \(N \geq 3\)

Cites Work

• Unnamed Item
• On the heat equation with concave-convex nonlinearity and initial data in weak-\(L^p\) spaces
• Well-posedness of one-phase Stefan problems for sublinear heat equations
• The heat equation with singular nonlinearity and singular initial data
• A singular parabolic equation with logarithmic nonlinearity and \(L^p\)-initial data
• Superlinear elliptic equations with singular coefficients on the boundary
• A semilinear parabolic system in a bounded domain
• Dual variational methods in critical point theory and applications
• Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations
• A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
• Remarks on sublinear elliptic equations
• A Cauchy problem for $u_t - \Delta u = u^p \ \hbox{with}\ 0 < p < 1$. Asymptotic behaviour of solutions
• Hardy inequalities in Orlicz spaces
• Hardy’s inequality and the boundary size
• On certain second order ordinary differential equations associated with Sobolev-Poincaré-type inequalities
• On the uniqueness and non‐uniqueness of solutions of initial value problems for some quasi‐linear parabolic equations

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