Rate estimates of gradient blowup for a heat equation with exponential nonlinearity

DOI10.1016/J.NA.2010.02.036zbMath1189.35033OpenAlexW2089578848WikidataQ116009518 ScholiaQ116009518MaRDI QIDQ972411

Bei Hu, Zhengce Zhang

Publication date: 25 May 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.02.036

zbMATH Keywords

one space dimensionnonlinear gradient source

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)

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Cites Work

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• Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem
• Blowup rate estimates for the heat equation with a nonlinear gradient source term
• Flat blow-up in one-dimensional semilinear heat equations
• Derivative blow-up and beyond for quasilinear parabolic equations
• Interior derivative blow-up for quasilinear parabolic equations
• Blowup rate for heat equation in Lipschitz domains with nonlinear heat source terms on the boundary
• Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions
• Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
• Asymptotics of blowup for a convection-diffusion equation with conservation
• Interior gradient blow-up in a semilinear parabolic equation
• Gradient blowup rate for a semilinear parabolic equation
• Blow-up behaviour of one-dimensional semilinear parabolic equations
• Convergence to a singular steady state of a parabolic equation with gradient blow-up
• Global solutions of inhomogeneous Hamilton-Jacobi equations
• The Role of Critical Exponents in Blowup Theorems
• Blow up for a diffusion-advection equation
• Asymptotically self‐similar blow‐up of semilinear heat equations
• Blow–Up Profiles in One–Dimensional. Semilinear Parabolic Problems
• Refined asymptotics for the blowup of u_t — δu = u^p
• On the interior derivative blow-up for the curvature evolution of capillary surfaces

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