L.M.P.A
Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

## Joachim von Below

• Equipe : Analyse
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

1. The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions ( and ), In Linear Algebra Appl., volume 439, 1792-1814, . [pdf]
2. Some remarks on the eigenvalue multiplicities of the Laplacian on infinite locally finite trees (, and ), In Results Math., volume 63, 1331-1350, . [pdf]
3. Eigenvalue asymptotics for second-order elliptic operators on networks ( and ), In Asymptot. Anal., volume 77, 147-167, .
4. The eigenvalues of the Laplacian on locally finite networks under generalized node transition ( and ), In Results Math., volume 54, 15-39, . [pdf]
5. Isospectral infinite graphs and networks and infinite eigenvalue multiplicities ( and ), In Netw. Heterog. Media, volume 4, 453-468, . [pdf]
6. An index theory for uniformly locally finite graphs (), In Linear Algebra Appl., volume 431, 1-19, . [pdf]
7. A characterization of even doubly-stochastic matrices ( and ), In Discrete Math., volume 309, 1273-1283, . [pdf]
8. Even and odd diagonals in doubly stochastic matrices ( and ), In Discrete Math., volume 308, 3917-3929, . [pdf]
9. Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up (, and ), In Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., volume 17, 35-67, . [pdf]
10. Spectral asymptotics for the Laplacian under an eigenvalue dependent boundary condition (), In Bull. Belg. Math. Soc. Simon Stevin, volume 12, 505-519, . [pdf]
11. The eigenvalues of the Laplacian on locally finite networks ( and ), In Results Math., volume 47, 199-225, .
12. Harmonic functions on locally finite networks ( and ), In Results Math., volume 45, 1-20, .
13. Blow up for reaction diffusion equations under dynamical boundary conditions ( and ), In Comm. Partial Differential Equations, volume 28, 223-247, . [pdf]
14. A qualitative theory for parabolic problems under dynamical boundary conditions ( and ), In J. Inequal. Appl., volume 5, 467-486, . [pdf]
15. Nonlinear degenerate elliptic equations and axially symmetric problems ( and ), In Calc. Var. Partial Differential Equations, volume 7, 41-51, . [pdf]
16. Dynamical interface transition in ramified media with diffusion ( and ), In Comm. Partial Differential Equations, volume 21, 255-279, . [pdf]
17. The index of a periodic graph (), In Results Math., volume 25, 198-223, .
18. Sturm-Liouville eigenvalue problems on networks (), In Math. Methods Appl. Sci., volume 10, 383-395, . [pdf]
19. Classical solvability of linear parabolic equations on networks (), In J. Differential Equations, volume 72, 316-337, . [pdf]
20. A characteristic equation associated to an eigenvalue problem on $c^2$-networks (), In Linear Algebra Appl., volume 71, 309-325, . [pdf]
21. On a theorem of L. Mirsky on even doubly-stochastic matrices (), In Discrete Math., volume 55, 311-312, . [pdf]

### Chapitres de livres

1. Eigenvalue asymptotics under a nondissipative eigenvalue dependent boundary condition for second-order elliptic operators (), Chapter in Functional analysis and evolution equations, Birkhäuser, 67-81, . [pdf]
2. Can one hear the shape of a network? (), Chapter in Partial differential equations on multistructures (Luminy, 1999), Dekker, volume 219, 19-36, .
3. 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, .
4. 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, .
5. 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, .
6. 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, .

### Rapports

1. Stability implies constancy on finite metric graphs ( and ), Technical report 527, LMPA, .
2. A variationnal approach to relativistic fluid balls ( and ), Technical report 508, LMPA, .
3. Instability of stationnary solutions of evolution equations on graphs under dynamical node transition ( and ), Technical report 503, LMPA, .
4. Instability of stationnary solutions of reaction-diffusion-equations on networks ( and ), Technical report 495, LMPA, .
5. The Spectrum of the Hilbert Space Valued Second Derivative with General Self-Adjoint Boundary Conditions ( and ), Technical report 478, LMPA, .
6. Some remarks on the eigenvalue multiplicities of the Laplacian on infinite locally finite trees (, and ), Technical report, LMPA, .
7. Eigenvalue multiplicities and asymptotics for second order elliptic operators on networks ( and ), Technical report, LMPA, .
8. Growth order and blow up points for the parabolic Burger's equation under dynamical boundary conditions (, and ), Technical report, LMPA, .
9. Eigenvalue multiplicities and asymptotics for second order elliptic operators on networks ( and ), Technical report, LMPA, .
10. A characterization of even doubly-stochastic matrices ( and ), Technical report, LMPA, .
11. Isospectral infinite graphs and infinite eigenvalue multiplicities ( and ), Technical report, LMPA, .
12. ?`Se puede oír la forma de una red ? (), Technical report, LMPA, .
13. Even and odd diagonals in doubly-stochastic matrices ( and ), Technical report, LMPA, .
14. An index theory for uniformly locally finite graphs (), Technical report, LMPA, .
15. On the rotating star problem in general relativity ( and ), Technical report, LMPA, .
16. Eigenvalue asymptotics under a non dissipative eigenvalue dependent boundary condition for second order elliptic operators ( and ), Technical report, LMPA, .
17. The eigenvalues of the Laplacian on locally finite networks under generalized node transition ( and ), Technical report, LMPA, .
18. Blow up for some nonlinear parabolic problems with convection under dynamical boundary conditions ( and ), Technical report, LMPA, .
19. Even and odd diagonals in doubly-stochastic matrices ( and ), Technical report, LMPA, .
20. Parabolic problems with dynamical boundary conditions : eigenvalue expansions and blow up (, and ), Technical report, LMPA, .
21. The eigenvalues of the Laplacian on locally finite networks ( and ), Technical report, LMPA, .
22. Spectral asymptotics for the Laplacian under an eigenvalue dependent boundary condition - II ( and ), Technical report, LMPA, .
23. Spectral asymptotics for the Laplacian under eigenvalue dependent boundary condition ( and ), Technical report, LMPA, .
24. Harmonic functions on locally finite networks ( and ), Technical report, LMPA, .
25. Blow up for reaction diffusion equations under dynamical boundary conditions ( and ), Technical report, LMPA, .
26. Can One Hear the Shape of a Network (), Technical report, LMPA, .
27. A maximum principle for fully nonlinear parabolic equations with time degeneracy (), Technical report, LMPA, .
28. A qualitative theory for parabolic problems under dynamical boundary conditions ( and ), Technical report, LMPA, .
29. Some spectral estimates for periodic graphs (, and ), Technical report, LMPA, .

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