Lower bounds for blow-up time in parabolic problems under Dirichlet conditions
By Lawrence E. Payne, Philip W. Schaefer. 2007
144 citations recorded by the source corpus.
We consider an initial-boundary value problem for the semilinear heat equation whose solution may blow up in finite time. We use a differential inequality technique to determine a lower bound on blow-up time if blow-up occurs. A second method based on a comparison principle is also presented.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/25b9fbfc6da6d1cee7957a1915e7021d0882b17b
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Numerical Analysis
Citations in the corpus
- Blow-up phenomena for some nonlinear parabolic problems (2008, background): “Introduction In a series of papers the authors have studied the phenomena of blow-up of solutions in initial-boundary value problems for nonlinear parabolic equations (see [3], [4], [5], [6]).”
- Bounds for blow-up time in nonlinear parabolic problems (2008, methodology): “A second method based on a comparison principle was also presented in [10].”
- Lower bounds for blow-up time in parabolic problems under Neumann conditions (2006, methodology): “Introduction In a recent paper [1], we considered the blow up phenomena for a nonnegative solution of an initial boundary value problem for the semilinear heat equation under a homogeneous Dirichlet boundary condition.”
- Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity (2015, background): “Furthermore, blow-up rate and blow-up time have been studied in [3,10,12].”
- Blow‐up phenomena for a pseudo‐parabolic equation (2015, unknown): “On the other hand, in [10, 11], Payne et al.”