Joachim von Below
- Grade : Professeur
- Equipe : Analyse
- Adresse : LMPA
Centre Universitaire de la Mi-Voix
50 rue F. Buisson
CS 80699
62228 Calais - Bureau : Universite du Littoral
- Email : Joachim.von-Below@univ-littoral.fr
- Téléphone : +33 3 21 46 36 53
Publications
Articles de revues
- Harmonic functions on metric graphs under the anti-Kirchhoff law ( ), In Results Math., volume 74, 36-28, 2019.
- Stability implies constancy for fully autonomous reaction-diffusion-equations on finite metric graphs ( ), In Netw. Heterog. Media, volume 13, 691-717, 2018.
- Instability of stationary solutions of reaction-diffusion-equations on graphs ( ), In Results Math., volume 68, 171-201, 2015.
- The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions ( ), In Linear Algebra Appl., volume 439, 1792-1814, 2013.
- Eigenvalue multiplicities for second order elliptic operators on networks ( ), In Oper. Matrices, volume 7, 587-602, 2013.
- Some remarks on the eigenvalue multiplicities of the Laplacian on infinite locally finite trees ( ), In Results Math., volume 63, 1331-1350, 2013.
- Eigenvalue asymptotics for second-order elliptic operators on networks ( ), In Asymptot. Anal., volume 77, 147-167, 2012.
- The eigenvalues of the Laplacian on locally finite networks under generalized node transition ( ), In Results Math., volume 54, 15-39, 2009.
- Isospectral infinite graphs and networks and infinite eigenvalue multiplicities ( ), In Netw. Heterog. Media, volume 4, 453-468, 2009.
- An index theory for uniformly locally finite graphs ( ), In Linear Algebra Appl., volume 431, 1-19, 2009.
- A characterization of even doubly-stochastic matrices ( ), In Discrete Math., volume 309, 1273-1283, 2009.
- Even and odd diagonals in doubly stochastic matrices ( ), In Discrete Math., volume 308, 3917-3929, 2008.
- Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up ( ), In Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., volume 17, 35-67, 2006.
- Spectral asymptotics for the Laplacian under an eigenvalue dependent boundary condition ( ), In Bull. Belg. Math. Soc. Simon Stevin, volume 12, 505-519, 2005.
- The eigenvalues of the Laplacian on locally finite networks ( ), In Results Math., volume 47, 199-225, 2005.
- Harmonic functions on locally finite networks ( ), In Results Math., volume 45, 1-20, 2004.
- Blow up for reaction diffusion equations under dynamical boundary conditions ( ), In Comm. Partial Differential Equations, volume 28, 223-247, 2003.
- A qualitative theory for parabolic problems under dynamical boundary conditions ( ), In J. Inequal. Appl., volume 5, 467-486, 2000.
- Nonlinear degenerate elliptic equations and axially symmetric problems ( ), In Calc. Var. Partial Differential Equations, volume 7, 41-51, 1998.
- Dynamical interface transition in ramified media with diffusion ( ), In Comm. Partial Differential Equations, volume 21, 255-279, 1996.
- The index of a periodic graph ( ), In Results Math., volume 25, 198-223, 1994.
- Sturm-Liouville eigenvalue problems on networks ( ), In Math. Methods Appl. Sci., volume 10, 383-395, 1988.
- Classical solvability of linear parabolic equations on networks ( ), In J. Differential Equations, volume 72, 316-337, 1988.
- A characteristic equation associated to an eigenvalue problem on $c^2$-networks ( ), In Linear Algebra Appl., volume 71, 309-325, 1985.
- On a theorem of L. Mirsky on even doubly-stochastic matrices ( ), In Discrete Math., volume 55, 311-312, 1985.
Chapitres de livres
- Instability of stationary solutions of evolution equations on graphs under dynamical node transition ( ), Chapter in Mathematical technology of networks, Springer, Cham, volume 128, 13-26, 2015.
- Eigenvalue asymptotics under a nondissipative eigenvalue dependent boundary condition for second-order elliptic operators ( ), Chapter in Functional analysis and evolution equations, Birkhäuser, 67-81, 2008.
- Can one hear the shape of a network? ( ), Chapter in Partial differential equations on multistructures (Luminy, 1999), Dekker, volume 219, 19-36, 2001.
- A maximum principle for fully nonlinear parabolic equations with time degeneracy ( ), Chapter in Evolution equations and their applications in physical and life sciences (Bad Herrenalb, 1998), Dekker, volume 215, 329-334, 2001.
- Front propagation in diffusion problems on trees ( ), Chapter in Calculus of variations, applications and computations (Pont-à-Mousson, 1994), Longman Sci. Tech., volume 326, 254-265, 1995.
- Nonlinear and dynamical node transition in network diffusion problems ( ), Chapter in Evolution equations, control theory, and biomathematics (Han sur Lesse, 1991), Dekker, volume 155, 1-10, 1994.
- An existence result for semilinear parabolic network equations with dynamical node conditions ( ), Chapter in Progress in partial differential equations: elliptic and parabolic problems (Pont-à-Mousson, 1991), Longman Sci. Tech., volume 266, 274-283, 1992.
- A maximum principle for semilinear parabolic network equations ( ), Chapter in Differential equations with applications in biology, physics, and engineering (Leibnitz, 1989), Dekker, volume 133, 37-45, 1991.
Rapports
- Stability implies constancy on finite metric graphs ( ), Technical report 527, LMPA, 2017.
- A variationnal approach to relativistic fluid balls ( ), Technical report 508, LMPA, 2014.
- Instability of stationnary solutions of evolution equations on graphs under dynamical node transition ( ), Technical report 503, LMPA, 2014.
- Instability of stationnary solutions of reaction-diffusion-equations on networks ( ), Technical report 495, LMPA, 2013.
- The Spectrum of the Hilbert Space Valued Second Derivative with General Self-Adjoint Boundary Conditions ( ), Technical report 478, LMPA, 2012.
- Some remarks on the eigenvalue multiplicities of the Laplacian on infinite locally finite trees ( ), Technical report, LMPA, 2012.
- Eigenvalue multiplicities and asymptotics for second order elliptic operators on networks ( ), Technical report, LMPA, 2011.
- Growth order and blow up points for the parabolic Burger's equation under dynamical boundary conditions ( ), Technical report, LMPA, 2010.
- Eigenvalue multiplicities and asymptotics for second order elliptic operators on networks ( ), Technical report, LMPA, 2010.
- A characterization of even doubly-stochastic matrices ( ), Technical report, LMPA, 2008.
- Isospectral infinite graphs and infinite eigenvalue multiplicities ( ), Technical report, LMPA, 2007.
- ?`Se puede oír la forma de una red ? ( ), Technical report, LMPA, 2007.
- Even and odd diagonals in doubly-stochastic matrices ( ), Technical report, LMPA, 2007.
- An index theory for uniformly locally finite graphs ( ), Technical report, LMPA, 2007.
- On the rotating star problem in general relativity ( ), Technical report, LMPA, 2006.
- Eigenvalue asymptotics under a non dissipative eigenvalue dependent boundary condition for second order elliptic operators ( ), Technical report, LMPA, 2006.
- The eigenvalues of the Laplacian on locally finite networks under generalized node transition ( ), Technical report, LMPA, 2006.
- Blow up for some nonlinear parabolic problems with convection under dynamical boundary conditions ( ), Technical report, LMPA, 2006.
- Even and odd diagonals in doubly-stochastic matrices ( ), Technical report, LMPA, 2005.
- Parabolic problems with dynamical boundary conditions : eigenvalue expansions and blow up ( ), Technical report, LMPA, 2005.
- The eigenvalues of the Laplacian on locally finite networks ( ), Technical report, LMPA, 2005.
- Spectral asymptotics for the Laplacian under an eigenvalue dependent boundary condition - II ( ), Technical report, LMPA, 2004.
- Spectral asymptotics for the Laplacian under eigenvalue dependent boundary condition ( ), Technical report, LMPA, 2003.
- Harmonic functions on locally finite networks ( ), Technical report, LMPA, 2003.
- Blow up for reaction diffusion equations under dynamical boundary conditions ( ), Technical report, LMPA, 2001.
- Can One Hear the Shape of a Network ( ), Technical report, LMPA, 2000.
- A maximum principle for fully nonlinear parabolic equations with time degeneracy ( ), Technical report, LMPA, 1999.
- A qualitative theory for parabolic problems under dynamical boundary conditions ( ), Technical report, LMPA, 1999.
- Some spectral estimates for periodic graphs ( ), Technical report 084, LMPA, 1999.