Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity

DOI10.1016/j.jde.2006.07.012zbMath1110.35029OpenAlexW2005775282MaRDI QIDQ859521

Yūki Naito, Takashi Suzuki

Publication date: 16 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.jde.2006.07.012

zbMATH Keywords

self-similar solutionscaling propertyblowup rateCauchy-Dirichlet problemsshrinking domains

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Critical exponents in context of PDEs (35B33) Variational methods for second-order elliptic equations (35J20)

Related Items (3)

Blowup profile for a complex valued semilinear heat equation ⋮ Blow-up sets for a complex-valued semilinear heat equation ⋮ Blow-up of radially symmetric solutions for a semilinear heat equation on hyperbolic space

Cites Work

• Blow up behavior of solutions for a semilinear heat equation with supercritical nonlinearity
• A bound for global solutions of semilinear heat equations
• Remarks on the Schrödinger operator with singular complex potentials
• Type-II blowup for a semilinear heat equation
• Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On blow-up rate for sign-changing solutions in a convex domain
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Nondegeneracy of blowup for semilinear heat equations
• Asymptotically self‐similar blow‐up of semilinear heat equations
• The zero set of a solution of a parabolic equation.
• On the Cauchy Problem for Reaction-Diffusion Equations
• On Nonexistence of type II blowup for a supercritical nonlinear heat equation
• Blow up rate for semilinear heat equations with subcritical nonlinearity
• Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball.
• Semilinear parabolic equations involving critical Sobolev exponent: Local and asymptotic behavior of solutions
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