In this paper, we nvestigate a class of nonlinear parabolic problems, known as viscous Hamilton–Jacobi-type problems. We establish conditions on data sufficient to insure that blow-up occurs in finite time. Moreover, conditions on data and geometry of the spatial domain are derived, ensuring the solution to exist for all time with exponential decay.
Blow-up and Decay Bounds in Hamilton–Jacobi-type Problems
MARRAS, MONICA;PIRO, STELLA
2014-01-01
Abstract
In this paper, we nvestigate a class of nonlinear parabolic problems, known as viscous Hamilton–Jacobi-type problems. We establish conditions on data sufficient to insure that blow-up occurs in finite time. Moreover, conditions on data and geometry of the spatial domain are derived, ensuring the solution to exist for all time with exponential decay.
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