Address   Prof. Dr. Bogdan-Vasile Matioc Universität Regensburg Fakultät für Mathematik 93040 Regensburg Email: bogdan.matioc@ur.de Office: Universitätsstraße 31              Office: M 120 Phone: +499419434289

Research interests

• Nonlinear and nonlocal partial differential equations
• Moving boundary problems: the Hele-Shaw, Muskat, and Stokes flows
• Free boundary problems: nonlinear water waves
• Degenerate equations and systems modeling thin fluid films
• Gradient flows in connection with Wasserstein metrics
• Geometric evolution equations

Research projects

• Research Training Group 2339 (RTG 2339) Interfaces, Complex Structures, and Singular Limits

Editorial board

• Annals of West University of Timisoara - Mathematics and Computer Science

PhD Students

• Daniel Böhme (since January 2023)

• Jonas Bierler (graduated Februaray 2022), Thesis: The multiphase Muskat problem in two dimensions

Submitted articles

• B.-V. Matioc, L. Roberti, and Ch. Walker, Quasilinear parabolic equations with superlinear nonlinearities in critical spaces,
  arXiv:2408.05067, 25pp.

Accepted articles

• B.-V. Matioc and Ch. Walker, Global solutions for semilinear parabolic evolution problems with Hölder continuous nonlinearities,
  arXiv:2404.11089, to appear in Bull. Lond. Math. Soc., 15pp.

• D. Böhme and B.-V. Matioc, Well-posedness and stability for the two-phase periodic quasistationary Stokes flow,
  Published version, arXiv:2406.07181, to appear in Interfaces Free Bound.

• B.-V. Matioc and Ch. Walker, Well-posedness of quasilinear parabolic equations in time-weighted spaces,
  arXiv:2312.07974 , to appear in Proc. Roy. Soc. Edinburgh Sect. A.

• B.-V. Matioc and E. Parau, Steady periodic hydroelastic waves in polar regions,
  Published version, arXiv:2402.03857, to appear in Water Waves.

• J. Bierler and B.-V. Matioc, The multiphase Muskat problem with general viscosities in two dimensions,
  arXiv:2202.12004, to appear in Adv. Differential Equations, 29pp.

• B.-V. Matioc and Ch. Walker, The nonlocal mean curvature flow of periodic graphs,
  arXiv:2207.07474, to appear in Ann. Scuola Norm. Sup. Pisa, 32pp.

Published articles

• J. Escher, A.-V. Matioc, and B.-V. Matioc, The Mullins-Sekerka problem via the method of potentials,
  Math. Nachr., 297: 1960-1977, 2024, Published version, arXiv:2308.06083.

• Ph. Laurençot and B.-V. Matioc, Bounded weak solutions to a class of degenerate cross-diffusion systems,
  Ann. H. Lebesgue., 6: 847-874, 2023, Published version, arXiv:2201.06479.

• B.-V. Matioc and G. Prokert, Capillarity driven Stokes flow: the one-phase problem as small viscosity limit,
  Z. Angew. Math. Phys., 74(6), 212, 2023, Published version, arXiv:2209.13376.

• B.-V. Matioc and L. Roberti, Weak and classical solutions to an asymptotic model for atmospheric flows,
  J. Differential Equations, 367:603–624, 2023, Published version, arXiv:2304.08985.

• Ph. Laurençot and B.-V. Matioc, Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems,
  Arch. Math. (Brno), 59(2):201-213, 2023, Published version, arXiv:2207.00361.

• A.-V. Matioc and B.-V. Matioc, A new reformulation of the Muskat problem with surface tension,
  J. Differential Equations, 350:308–335, 2023, Published version, arXiv:2203.13567.

• Ph. Laurençot and B.-V. Matioc, The porous medium equation as a singular limit of the thin film Muskat problem,
  Asymptot. Anal., 131(2):255-271, 2023, Published version, arXiv:2108.09032.

• B.-V. Matioc and G. Prokert, Two-phase Stokes flow by capillarity in the plane: The case of different viscosities,
  NoDEA Nonlinear Differential Equations Appl., 29(5): Art. 54, 34 pp., 2022 Published version, arXiv:2102.12814.

• Ph. Laurençot and B.-V. Matioc, Bounded weak solutions to the thin film Muskat problem via an infinite family of Liapunov functionals,
  Trans. Amer. Math. Soc., 375(8):5963–5986, 2022, Published version, arXiv:2110.01234.

• J. Bierler and B.-V. Matioc, The multiphase Muskat problem with equal viscosities in two dimensions,
  Interfaces Free Bound., 24(2):163-196, 2022, Published version, arXiv:2101.07728.

• H. Abels and B.-V. Matioc, Well-posedness of the Muskat problem in subcritical Lp-Sobolev spaces,
  European J. Appl. Math., 33(2):224-266, 2022, Published version, arXiv:2003.07656.

• B.-V. Matioc and G. Prokert, Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials,
  Proc. Roy. Soc. Edinburgh Sect. A, 151:1815-1845, 2021, Published version, arXiv:2003.14010.

• A.-V. Matioc and B.-V. Matioc, The Muskat problem with surface tension and equal viscosities in subcritical Lp-Sobolev spaces,
  J. Elliptic Parabol. Equ., 7:635-670, 2021, Published version, arXiv:2010.12261.

• H. Garcke and B.-V. Matioc, On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces,
  J. Evol. Equ., 21:201-224, 2021, Published version, arXiv:1905.09675.

• J. Escher, P. Knopf, C. Lienstromberg, and B.-V. Matioc, Stratified periodic water waves with singular density gradients,
  Ann. Mat. Pura Appl., 199(5):1923-1959, 2020, Published version, arXiv:1911.13046.

• B.-V. Matioc, Well-posedness and stability results for some periodic Muskat problems,
  J. Math. Fluid Mech., 22(3): Art. 31, 45 pp., 2020, Published version, arXiv:1804.10403.

• B.-V. Matioc and Ch. Walker, On the principle of linearized stability in interpolation spaces for quasilinear evolution equations,
  Monatsh. Math., 191:615-634, 2020, Published version, arXiv:1804.10523.

• A.-V. Matioc and B.-V. Matioc, Well-posedness and stability results for a quasilinear periodic Muskat problem,
  J. Differential Equations, 266(9):5500–5531, 2019, arXiv:1706.09260.

• B.-V. Matioc, The Muskat problem in 2D: equivalence of formulations, well-posedness, and regularity results,
  Analysis & PDE, 12(2):281–332, 2019, arXiv:1610.05546.

• B.-V. Matioc, Viscous displacement in porous media: the Muskat problem in 2D,
  Trans. Amer. Math. Soc., 370(10):7511-7556, 2018, arXiv:1701.00992.

• J. Escher, B.-V. Matioc, and Ch. Walker, The domain of parabolicity for the Muskat problem,
  Indiana Univ. Math. J., 67(2):679–737, 2018, arXiv:1507.02601.

• Ph. Laurençot and B.-V. Matioc, Finite speed of propagation and waiting time for a thin film Muskat problem,
  Proc. Roy. Soc. Edinburgh Sect. A, 147(4):813–830, 2017, arXiv:1509.09100.

• Ph. Laurençot and B.-V. Matioc, Self-similarity in a thin film Muskat problem,
  SIAM J. Math. Anal., 49(4):2790–2842, 2017, arXiv:1409.7329.

• C. I. Martin and B.-V. Matioc, Gravity water flows with discontinuous vorticity and stagnation points,
  Commun. Math. Sci., 14(2): 415-441, 2016, arXiv:1503.01335.

• B.-V. Matioc, Recovery of Stokes waves from velocity measurements on an axis of symmetry,
  J. Phys. A, 48:255501(8pp), 2015, arXiv:1505.02502.

• B.-V. Matioc, A characterization of the symmetric steady water waves in terms of the underlying flow,
  Discrete Contin. Dyn. Syst. Ser. A, 34(8):3125-3133, 2014, arXiv:1401.6019.

• B.-V. Matioc, Non-uniform continuity of the semiflow map associated to the porous medium equation,
  Bull. Lond. Math. Soc., 46:1105-1115, 2014, arXiv:1401.1115.

• N. Duruk Mutlubaş, A. Geyer, and B.-V. Matioc, Non-uniform continuity of the flow map for an evolution equation
  modeling shallow water waves of moderate amplitude,
  Nonlinear Anal. Real World Appl., 17:322-331, 2014, arXiv:1312.3753.

• C. I. Martin and B.-V. Matioc, Steady periodic water waves with unbounded vorticity: equivalent formulations and existence results,
  J. Nonlinear Sci., 24:633-659, 2014, arXiv:1311.6935.

• A.-V. Matioc and B.-V. Matioc, Capillary-gravity water waves with discontinuous vorticity: existence and regularity results,
  Comm. Math. Phys., 330:859-886, 2014, arXiv:1311.6593.

• J. Escher and B.-V. Matioc, On the analyticity of periodic gravity water waves with integrable vorticity function,
  Differential Integral Equations, 27(3-4):217–232, 2014, arXiv:1311.6288.

• C. I. Martin and B.-V. Matioc, Existence of capillary-gravity water waves with piecewise constant vorticity,
  J. Differential Equations, 256(8):3086-3114, 2014, arXiv:1302.5523.

• J. Escher and B.-V. Matioc, Non-negative global weak solutions for a degenerated
  parabolic system approximating the two-phase Stokes problem,
  J. Differential Equations, 256(8):2659-2676, 2014, arXiv:1210.6457.

• Ph. Laurençot and B.-V. Matioc, A thin film approximation of the Muskat problem with gravity and capillary forces,
  J. Math. Soc. Japan, 66(4):1043-1071, 2014, arXiv:1206.5600.

• B.-V. Matioc, Global bifurcation for water waves with capillary effects and constant vorticity,
  Monatsh. Math., 174:459-475, 2014.

• D. Henry and B.-V. Matioc, On the existence of steady periodic capillary-gravity stratified water waves,
  Ann. Scuola Norm. Sup. Pisa, XII(4):955-974, 2013, arXiv:1305.5802.

• M. Ehrnström, J. Escher, and B.-V. Matioc, Steady-state fingering patterns for a periodic Muskat problem,
  Methods Appl. Anal., 20(1):33-46, 2013, arXiv:1303.6724.

• C. I. Martin and B.-V. Matioc, Existence of Wilton ripples for water waves with constant vorticity and capillary effects,
  SIAM J. Appl. Math., 73(4):1582-1595, 2013.

• A.-V. Matioc and B.-V. Matioc, On the symmetry of periodic gravity water waves with vorticity,
  Differential Integral Equations, 26(1-2):129-140, 2013.

• B.-V. Matioc, Regularity results for deep-water waves with Hölder continuous vorticity,
  Appl. Anal., 92(10):2144-2151, 2013.

• J. Escher, A.-V. Matioc, and B.-V. Matioc, Thin film approximations of the two-phase Stokes problem,
  Nonlinear Anal., 73:1-13, 2013.

• Ph. Laurençot and B.-V. Matioc, A gradient flow approach to a thin film approximation of the Muskat problem,
  Calc. Var. Partial Differential Equations, 47:319-341, 2013, arXiv:1110.6262.

• J. Escher and B.-V. Matioc, Existence and stability of solutions for a strongly coupled systems modelling thin fluid threads,
  NoDEA Nonlinear Differential Equations Appl., 20:539-555, 2013.

• B.-V. Matioc and G. Prokert, Hele-Shaw flow in thin threads: A rigorous limit result,
  Interfaces Free Bound., 14:205-230, 2012, arXiv:1207.3089.

• A.-V. Matioc and B.-V. Matioc, On periodic water waves with Coriolis effects and isobaric streamlines,
  J. Nonlinear Math. Phys., 19(supp01):1240009, 15pp, 2012, arXiv:1204.4993.

• B.-V. Matioc, Non-negative global weak solutions for a degenerate parabolic system modeling thin films driven by capillarity,
  Proc. Roy. Soc. Edinburgh Sect. A, 142A:1071-1085, 2012, arXiv:1110.6793.

• A.-V. Matioc and B.-V. Matioc, Regularity and symmetry properties of rotational solitary water waves,
  J. Evol. Equ., 12:481-494, 2012.

• J. Escher, A.-V. Matioc, and B.-V. Matioc, A generalised Rayleigh-Taylor condition for the Muskat problem,
  Nonlinearity, 20(1):73-92, 2012, arXiv:1005.2511.

• B.-V. Matioc, On the regularity of deep-water waves with general vorticity distributions,
  Quart. Appl. Math., LXX(2):393-405, 2012.

• J. Escher, A.-V. Matioc, and B.-V. Matioc, Modelling and analysis of the Muskat problem for thin fluid layers,
  J. Math. Fluid Mech., 14(2):267-277, 2012.

• D. Henry and B.-V. Matioc, On the regularity of steady periodic stratified water waves,
  Commun. Pure Appl. Anal., 11(4):1453-1464, 2012.

• J. Escher, Ph. Laurençot, and B.-V. Matioc, Existence and stability of weak solutions for a degenerate
  parabolic system modelling two-phase flows in porous media,
  Ann. Inst. H. Poincaré Anal. Non Linéaire, 28(4):583-598, 2011, arXiv:1101.3964.

• J. Escher and B.-V. Matioc, On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results,
  Z. Anal. Anwend., 30(2):193-218, 2011, arXiv:1005.2512.

• J. Escher, A.-V. Matioc, and B.-V. Matioc, On stratified steady periodic water waves with linear density distribution and stagnation points,
  J. Differential Equations, 251:2932-2949, 2011.

• J. Escher and B.-V. Matioc, Stability properties of non-radial steady ferrofluid patterns,
  Comm. Partial Differential Equations, 36(3):363-379, 2011.

• B.-V. Matioc, Analyticity of the streamlines for periodic traveling water waves with bounded vorticity,
  Int. Math. Res. Not., 17:3858-3871, 2011.

• M. Ehrnström, J. Escher, and B.-V. Matioc, Well-posedness, instabilities, and bifurcation results for the flow in a rotating Hele-Shaw cell,
  J. Math. Fluid Mech., 13(2):271-293, 2011.

• J. Escher and B.-V. Matioc, Neck pinching for periodic mean curvature flows,
  Analysis (Munich), 30(3):253-260, 2010.

• J. Escher, A.-V. Matioc, and B.-V. Matioc, Classical solutions and stability results for Stokesian Hele-Shaw flows,
  Ann. Scuola Norm. Sup. Pisa, IX:325-349, 2010.

• J. Escher, A.-V. Matioc, and B.-V. Matioc, Analysis of a ferrofluid in a radial magnetic field,
  An. Univ. Vest Timis. Ser. Mat.-Inform., XLVII(3): 27-44, 2009.

• M. Ehrnström, J. Escher, and B.-V. Matioc, Two dimensional steady edge waves. Part II: Solitari waves,
  Wave Motion, 46(6):372-378, 2009.

• M. Ehrnström, J. Escher, and B.-V. Matioc, Two dimensional steady edge waves. Part I: Periodic waves,
  Wave Motion, 46(6):363-371, 2009.

• J. Escher and B.-V. Matioc, A moving boundary problem for periodic Stokesian Hele-Shaw flows,
  Interfaces Free Bound., 11:119-137, 2009.

• J. Escher and B.-V. Matioc, Multidimensional Hele-Shaw flows modelling Stokesian fluids,
  Math. Methods Appl. Sci., 32:577-593, 2009.

• J. Escher and B.-V. Matioc, Stability of the equilibria for periodic Stokesian Hele-Shaw flows,
  J. Evol. Equ., 8(3):513-522, 2008.

• J. Escher and B.-V. Matioc, On periodic Stokesian Hele-Shaw flows with surface tension,
  European J. Appl. Math., 19(6):717-734, 2008.

• J. Escher and B.-V. Matioc, Existence and stability results for periodic Stokesian Hele-Shaw flows,
  SIAM J. Math. Anal., 40(5):1992-2006, 2008.

• B.-V. Matioc, Boundary value problems for rotationally symmetric mean curvature flows,
  Arch. Math., 89:365-372, 2007.

Articles in proceedings

• D. Böhme and B.-V. Matioc, Recovery of traveling water waves with smooth vorticity
  from the horizontal velocity on a line of symmetry for various wave regimes,
  In: Henry, D. (eds) Nonlinear Dispersive Waves.
  Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham, 2024. Published version, arXiv:2308.02244.

• D. Henry and B.-V. Matioc, Aspects of the mathematical analysis of nonlinear stratified water waves,
  Elliptic and Parabolic Equations, Springer Proceedings in Mathematics and Statistics,
  vol. 119, Springer International Publishing, 2015, 159-177.

• J. Escher and B.-V. Matioc, Analyticity of rotational water waves,
  Elliptic and Parabolic Equations, Springer Proceedings in Mathematics and Statistics,
  vol. 119, Springer International Publishing, 2015, 111-137.

• J. Escher, Ph. Laurençot, and B.-V. Matioc, Thin film approximations to the Muskat problem,
  Équations aux dérivées partielles et leurs applications, Le Havre 2012, 83-91,
  FNM Fédération Normandie Mathématiques, Paris France 2013.

• J. Escher, A.-V. Matioc, and B.-V. Matioc, Analysis of a mathematical model describing necrotic tumor growth,
  Modelling, simulation and software concepts for scientific-technological problems, 237-250,
  Lect. Notes Appl. Comput. Mech. 57, Springer, Berlin, 2011.

Education

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