Classification of blow-up with nonlinear diffusion and localized reaction

DOI10.1016/j.jde.2006.04.017zbMath1110.35034OpenAlexW2156054212MaRDI QIDQ859505

Raúl Ferreira, Juan Luis Vazquez, Arturo de Pablo

Publication date: 16 January 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://eprints.ucm.es/12493/1/2006classification-13.pdf

zbMATH Keywords

nonnegative solutionsporous media equationblow-up ratesblow-up profilesblow-up sets

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for second-order parabolic equations (35K15)

Related Items

Self-similar blow-up profiles for a reaction-diffusion equation with critically strong weighted reaction ⋮ Asymptotic analysis for a localized nonlinear diffusion equation ⋮ Asymptotic behavior of the nonlocal diffusion equation with localized source ⋮ On approximate solutions to the Neumann elliptic boundary value problem with non-linearity of exponential type ⋮ A nonlinear diffusion equation with reaction localized in the half-line ⋮ On regularization of an optimal control problem for ill-posed nonlinear elliptic equations ⋮ The Liouville theorem of a torsion system and its application to symmetry group of a porous medium type equation on symmetric spaces ⋮ Self-similar blow-up patterns for a reaction-diffusion equation with weighted reaction in general dimension ⋮ ASYMPTOTIC BEHAVIOR OF THE BLOW-UP AND GLOBAL EXISTENCE FOR A PARABOLIC EQUATION INVOLVING A CRITICAL EXPONENT ⋮ Critical exponents for the evolution \(p\)-Laplacian equation with a localized reaction ⋮ Optimal existence, uniqueness and blow-up for a quasilinear diffusion equation with spatially inhomogeneous reaction ⋮ Cauchy problem for fast diffusion equation with localized reaction ⋮ Blow-up patterns for a reaction-diffusion equation with weighted reaction in general dimension ⋮ Self-similar solutions preventing finite time blow-up for reaction-diffusion equations with singular potential ⋮ Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction ⋮ Fujita exponent for a nonlinear degenerate parabolic equation with localized source ⋮ Critical nonlinearities in partial differential equations ⋮ On optimal control problem for an ill-posed strongly nonlinear elliptic equation with \(p\)-Laplace operator and \(L^1\)-type of nonlinearity ⋮ Critical nonlinearities in partial differential equations ⋮ Cauchy problem for the non-Newtonian polytropic filtration equation with a localized reaction ⋮ On Neumann boundary control problem for ill-posed strongly nonlinear elliptic equation with \(p\)-Laplace operator and \(L^1\)-type of nonlinearity ⋮ Blow-up with logarithmic nonlinearities ⋮ Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions ⋮ Blow up profiles for a reaction-diffusion equation with critical weighted reaction ⋮ Grow-up for a quasilinear heat equation with a localized reaction ⋮ Weighted \(L^p\) estimates and Fujita exponent for a nonlocal equation ⋮ Effects of reactive gradient term in a multi-nonlinear parabolic problem ⋮ Separate variable blow-up patterns for a reaction-diffusion equation with critical weighted reaction ⋮ Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction with linear growth

Cites Work

• Unnamed Item
• Unnamed Item
• Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
• Complete blow-up after \(T_{\max}\) for the solution of a semilinear heat equation
• Some existence and nonexistence theorems for solutions of degenerate parabolic equations
• Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source
• The blow-up profile for a fast diffusion equation with a nonlinear boundary condition
• The problem of blow-up in nonlinear parabolic equations
• Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
• On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary
• The role of critical exponents in blow-up theorems: The sequel
• Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions
• The Role of Critical Exponents in Blowup Theorems
• On the blow-up set for u_t=du^m+u^m, m>1
• A general approach to critical Fujita exponents in nonlinear parabolic problems
• A diffusion equation with localized chemical reactions
• Blow-up for quasilinear heat equations with critical Fujita's exponents
• Asymptotic simplification for a reaction-diffusion problem with a nonlinear boundary condition
• The critical exponents of parabolic equations and blow-up inRⁿ
• On Asymptotic Self-Similar Behaviour for a Quasilinear Heat Equation: Single Point Blow-Up