Concepedia

LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS

Glasgow Mathematical Journal · 2011 · 24 citations · 8 references

Open access

Concepts

Numerical AnalysisFree Boundary ProblemFinite TimeHyperbolic Conservation LawParabolic EquationBlow-up TimeNonlinear Hyperbolic ProblemHyperbolic EquationLower Bounds

Abstract

Abstract This paper deals with some non-linear initial-boundary value problems under homogeneous Neumann boundary conditions, in which the solutions may blow up in finite time. Using a first-order differential inequality technique, lower bounds for blow-up time are determined.

References

8

REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS

J. M. Ball · The Quarterly Journal of Mathematics · 1977 · 518 citations

Lim P, Parabolic Equation, Nonlinear Hyperbolic Problem +5

The problem Of blow-up in nonlinear parabolic equations

Victor A. Galaktionov, Juan Luís Vázquez · Discrete and Continuous Dynamical Systems · 2002 · 386 citations

Parabolic Equation, Nonlinear Parabolic Equations, Nonlinear Hyperbolic Problem +5

Lower bounds for blow-up time in parabolic problems under Dirichlet conditions

L. E. Payne, Philip Schaefer · Journal of Mathematical Analysis and Applications · 2006 · 136 citations

Dirichlet Form, Hyperbolic Conservation Law, Parabolic Equation +5

Lower bounds for blow-up time in parabolic problems under Neumann conditions

L. E. Payne, Philip Schaefer · Applicable Analysis · 2006 · 122 citations

Numerical Analysis, Free Boundary Problem, Hyperbolic Conservation Law +8

Blow-up phenomena for some nonlinear parabolic problems

L. E. Payne, G. A. Philippin, Philip Schaefer · Nonlinear Analysis · 2007 · 113 citations

Blow-up Phenomena, Hyperbolic Conservation Law, Nonlinear Hyperbolic Problem +1