0000000001157075

AUTHOR

Luigi Orsina

showing 2 related works from this author

Existence results for $L^1$ data of some quasi-linear parabolic problems with a quadratic gradient term and source

2002

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.

Quadratic equationApplied MathematicsModeling and SimulationWeak solutionMathematical analysisParabolic problemGeodetic datumQuasi linearLower orderParabolic partial differential equationTerm (time)Mathematics
researchProduct

Quasilinear elliptic equations with singular quadratic growth terms

2011

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

Quadratic growthnonlinear elliptic equations; natural growth condition; vertical asymptote; measure dataApplied MathematicsGeneral MathematicsMathematical analysisOpen setmeasure dataFunction (mathematics)nonlinear elliptic equationsBounded functionvertical asymptoteStandard probability spacenatural growth conditionAsymptoteValue (mathematics)Mathematics
researchProduct