0000000000786193

AUTHOR

Jean-baptiste Casteras

showing 4 related works from this author

Translating Solitons Over Cartan-Hadamard Manifolds

2020

We prove existence results for entire graphical translators of the mean curvature flow (the so-called bowl solitons) on Cartan-Hadamard manifolds. We show that the asymptotic behaviour of entire solitons depends heavily on the curvature of the manifold, and that there exist also bounded solutions if the curvature goes to minus infinity fast enough. Moreover, it is even possible to solve the asymptotic Dirichlet problem under certain conditions.

Mathematics - Differential GeometryTranslating graphsmean curvature equationTranslating solitonsRiemannin monistotdifferentiaaligeometriaDifferential Geometry (math.DG)FOS: Mathematics111 MathematicsHadamard manifoldGeometry and TopologyMathematics::Differential Geometrymonistottranslating graphsCartan-Hadamard manifold53C21 53C44
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Strong Instability of Ground States to a Fourth Order Schrödinger Equation

2019

Abstract In this note, we prove the instability by blow-up of the ground state solutions for a class of fourth order Schrödinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic nonlinear Schrödinger due to Boulenger and Lenzmann [8] and confirm numerical conjectures from [1–3, 11].

General Mathematics010102 general mathematicsMathematics::Analysis of PDEs01 natural sciencesInstabilitySchrödinger equationsymbols.namesakeNonlinear systemFourth ordersymbolsBiharmonic equation[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsGround stateSchrödinger's catComputingMilieux_MISCELLANEOUSMathematicsMathematical physicsSciences exactes et naturelles
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Normalized solutions to the mixed dispersion nonlinear Schr��dinger equation in the mass critical and supercritical regime

2019

In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation γΔ2u − Δu + αu =

Applied MathematicsGeneral Mathematics010102 general mathematics01 natural sciencesSupercritical fluid010101 applied mathematicssymbols.namesakeMathématiquesMathematics - Analysis of PDEsEquations différentielles et aux dérivées partiellesQuantum electrodynamicsDispersion (optics)symbolsFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsAnalyse mathématiqueNonlinear Schrödinger equationComputingMilieux_MISCELLANEOUSMathematicsAnalysis of PDEs (math.AP)
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Non-parametric mean curvature flow with prescribed contact angle in Riemannian products

2020

Assuming that there exists a translating soliton $u_\infty$ with speed $C$ in a domain $\Omega$ and with prescribed contact angle on $\partial\Omega$, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to $u_\infty +Ct$ as $t\to\infty$. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of $\Omega$ and Ricci curvature in $\Omega$.

Mathematics - Differential GeometryApplied MathematicsMean curvature flowdifferentiaaligeometriamean curvature flowDifferential Geometry (math.DG)FOS: Mathematics111 MathematicsGeometry and TopologyMathematics::Differential Geometryprescribed contact angletranslating graphs53C21 53E10Analysis
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