Growth estimates in diffusion-reaction problems

DOI10.1007/BF00250475zbMath0452.35059OpenAlexW2025362922MaRDI QIDQ1148464

Rene P. Sperb

Publication date: 1981

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00250475

zbMATH Keywords

a priori estimatesreaction-diffusion problemsnonlinear parabolic problemsparabolic maximum principle

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Maximum principles in context of PDEs (35B50) A priori estimates in context of PDEs (35B45)

Related Items (10)

Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities ⋮ Maximum principles and nonlinear elliptic problems ⋮ New life-span results for the nonlinear heat equation ⋮ Quasilinear heat equations with first-order sign-invariants and new explicit solutions ⋮ Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations ⋮ Some extremum principles in semilinear parabolic problems ⋮ Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity ⋮ Nonlinear diffusion-reaction problems with time-dependent diffusion coefficient ⋮ Blow-up solutions for a class of nonlinear parabolic equations with Dirichlet boundary conditions ⋮ Blow-up of solutions for a class of semilinear reaction diffusion equations with mixed boundary conditions.

Cites Work

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• Positive eigenfunctions for \(\Delta u+\lambda f(u) = 0\)
• Maximum principles and nonlinear elliptic problems
• Isoperimetric inequalities for a class of nonlinear parabolic equations
• Maximum principles for some functionals associated with the solution of elliptic boundary value problems
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• Pointwise bounds for solutions of semilinear parabolic equations
• Topics in stability and bifurcation theory
• On the growth of solutions of quasi‐linear parabolic equations

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