Some Blowup Results for a Nonlinear Parabolic Equation with a Gradient Term
Open Access
- 1 July 1989
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 20 (4) , 886-907
- https://doi.org/10.1137/0520060
Abstract
Under some conditions, a blowup result is proved for the solution $u$ of: [egin{gathered} u_t = Delta u - left| {
abla u}
ight|^q + left| {u}
ight|^{p - 1} u,quad t > 0,quad x in Omega hfill \ u(t,x) = 0,quad t > 0,quad x in Gamma , hfill \ u(0,x) = varphi (x),quad x in Omega . hfill \ end{gathered} ] The associated elliptic problem is also studied. ©1989 Society for Industrial and Applied Mathematic
Keywords
This publication has 27 references indexed in Scilit:
- Observations on blow up and dead cores for nonlinear parabolic equationsMathematische Zeitschrift, 1989
- Nonexistence for the Kassoy ProblemSIAM Journal on Mathematical Analysis, 1987
- A Criterion for Blow-Up of Solutions to Semilinear Heat EquationsSIAM Journal on Mathematical Analysis, 1987
- The Blow-Up Time for Solutions of Nonlinear Heat Equations with Small DiffusionSIAM Journal on Mathematical Analysis, 1987
- The Existence of Bounded Solutions of a Semilinear Heat EquationSIAM Journal on Mathematical Analysis, 1987
- A bound for global solutions of semilinear heat equationsCommunications in Mathematical Physics, 1986
- Global blow-up of a nonlinear heat equationProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1986
- The form of blow-up for nonlinear parabolic equationsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984
- Symmetry and related properties via the maximum principleCommunications in Mathematical Physics, 1979
- Fractional powers of operatorsPacific Journal of Mathematics, 1966