6533b862fe1ef96bd12c62be
RESEARCH PRODUCT
Existence results for $L^1$ data of some quasi-linear parabolic problems with a quadratic gradient term and source
Lucio BoccardoSergio Segura De LeónFuensanta AndreuLuigi Orsinasubject
Quadratic equationApplied MathematicsModeling and SimulationWeak solutionMathematical analysisParabolic problemGeodetic datumQuasi linearLower orderParabolic partial differential equationTerm (time)Mathematicsdescription
In this paper we deal with a Cauchy–Dirichlet quasilinear parabolic problem containing a gradient lower order term; namely, ut - Δu + |u|2 γ-2u |∇u|2 = |u|p-2u. We prove that if p ≥ 1, γ ≥ ½ and p < 2 γ + 2, then there exists a global weak solution for all initial data in L1 (Ω). We also see that there exists a non-negative solution if the initial datum is non-negative.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-01-01 |