Blow-up and global existence for the inhomogeneous porous medium equation with reaction

zbMath1465.35072arXiv2007.12005MaRDI QIDQ4989047

Fabio Punzo, Giulia Meglioli

Publication date: 20 May 2021

Full work available at URL: https://arxiv.org/abs/2007.12005

zbMATH Keywords

sub-supersolutionspower-like reaction term

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic equations (35K15) Blow-up in context of PDEs (35B44) Comparison principles in context of PDEs (35B51) Quasilinear parabolic equations (35K59)

Related Items

Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients

Cites Work

• Unnamed Item
• On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density
• Dirichlet conditions at infinity for parabolic and elliptic equations
• On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes
• Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincaré inequalities
• On the Cauchy problem for nonlinear parabolic equations with variable density
• Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds
• Uniqueness and nonuniqueness of solutions to parabolic problems with singular coefficients
• On the uniqueness of bounded solutions to singular parabolic problems
• Blow-up and global existence for solutions to the porous medium equation with reaction and slowly decaying density
• The Cauchy problem for the inhomogeneous porous medium equation
• Fractional porous media equations: existence and uniqueness of weak solutions with measure data
• The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium
• Criteria for well-posedness of degenerate elliptic and parabolic problems
• On the Cauchy problem for a class of parabolic equations with variable density
• Blow-up and global existence for the porous medium equation with reaction on a class of Cartan-Hadamard manifolds
• The Cauchy problem for a nonhomogeneous heat equation with reaction
• Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density
• Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction with linear growth
• Universal bounds at the blow-up time for nonlinear parabolic equations
• The Cauchy problem for a degenerate parabolic equation with inhomogeneous density and source in the class of slowly decaying initial data
• Admissible conditions for parabolic equations degenerating at infinity
• Propagation of thermal waves in an inhomogeneous medium
• Non-linear diffusion in a finite mass medium
• Nonlinear thermal evolution in an inhomogeneous medium
• The Filtration Equation in a Class of Functions Decreasing at Infinity
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions
• On nonexistence of global solutions of some semilinear parabolic differential equations
• Critical Fujita exponents of degenerate and singular parabolic equations
• Prescribed conditions at infinity for parabolic equations
• Blow-up of nonnegative solutions to quasilinear parabolic inequalities