Institut für Angewandte Analysis

Monograph
 
  • Prüss, J.; Schnaubelt, R.; Zacher, R.: Mathematische Modelle in der Biologie. Deterministische homogene Systeme. Mathematik kompakt. Birkhäuser, Basel, 2008
 

Refereed Articles
 
  1. Zacher, R.: Persistent solutions for age-dependent pair-formation models. J. Math. Biol. 42 (2001), 507-531.
  2. Zacher, R.: Maximal regularity of type Lp for abstract parabolic Volterra equations. J. Evol. Equ. 5 (2005), 79-103.
  3. Prüss, J.; Pujo-Menjouet, L.; Webb, G. F.; Zacher, R.: Analysis of a model for the dynamics of prions. Discrete Contin. Dyn. Syst. Ser. B 6 (2006), 225-235.
  4. Zacher, R.: Quasilinear parabolic integro-differential equations with nonlinear boundary conditions. Differential Integral Equations 19 (2006), 1129-1156.
  5. Zacher, R.: A weak Harnack inequality for fractional differential equations. J. Integral Equations Appl. 19 (2007), 209-232.
  6. Gerisch, A.; Kotschote, M.; Zacher, R.: Well-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology. NoDEA Nonlinear Differential Equations Appl. 14 (2007), 593-624.
  7. Vergara, V.; Zacher, R.: Lyapunov functions and convergence to steady state for differential equations of fractional order. Math. Z. 259 (2008), 287-309.
  8. Clément, Ph.; Zacher, R.: Global smooth solutions to a fourth-order quasilinear fractional evolution equation. Functional Analysis and evolution equations, 131-146, Birkhäuser, Basel, 2008.
  9. Prüss, J.; Schnaubelt, R.; Zacher, R.: Global asymptotic stability of equilibria in models for virus dynamics. Math. Model. Nat. Phenom. 3 (2008), 126-142.
  10. Zacher, R.: Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients. J. Math. Anal. Appl. 348 (2008), 137-149.
  11. Denk, R.; Prüss, J.; Zacher, R.: Maximal Lp-regularity of parabolic problems with boundary dynamics of relaxation type. Journal of Functional Analysis 255 (2008), 3149-3187.
  12. Prüss J.; Simonett, G.; Zacher, R.: On convergence of solutions to equilibria for quasilinear parabolic problems. J. Differential Equations 246 (2009), 3902-3931.
  13. Zacher, R.: Weak solutions of abstract evolutionary integro-differential equations in Hilbert spaces. Funkcialaj Ekvacioj 52 (2009), 1-18.
  14. Alabau-Boussouira, F.; Prüss, J.; Zacher, R.: Exponential and polynomial stability of a wave equation for boundary memory damping with singular kernels. C. R. Acad. Sci. Paris Sér. I 347 (2009), 277-282.
  15. Zacher, R.: Convergence to equilibrium for second order differential equations with weak damping of memory type. Adv. Differential Equations 14 (2009), 749-770.
  16. Prüss J.; Simonett, G.; Zacher, R.: On normal stability for nonlinear parabolic equations. Discrete Contin. Dyn. Syst. Supplement 2009, 612-621.
  17. Prüss, J.; Vergara, V.; Zacher, R.: Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory. Discrete Contin. Dyn. Syst. Ser. A. 26 (2010), 625-647.
  18. Vergara, V.; Zacher, R.: A priori bounds for degenerate and singular evolutionary partial integro-differential equations. Nonlinear Analysis 73 (2010), 3572--3585.
  19. Zacher, R.: The Harnack inequality for the Riemann-Liouville fractional derivation operator. Math. Inequal. Appl. 14 (2011), 35--43.
  20. Winkert, P.; Zacher, R.: A priori bounds for weak solutions to elliptic equations with nonstandard growth. Discrete Contin. Dyn. Syst. S. 5 (2012), 865-878.
  21. Zacher, R.: Global strong solvability of a quasilinear subdiffusion problem. J. Evol. Equ. 12 (2012), 813-831.
  22. Prüss J.; Simonett, G.; Zacher, R.: Qualitative behaviour of solutions for thermodynamically consistent Stefan problems with surface tension. Arch. Ration. Mech. Anal. 207 (2013), 611-667.
  23. Zacher, R.: A De Giorgi-Nash type theorem for time fractional diffusion equations. Math. Ann. 356 (2013), 99-146.
  24. Zacher, R.: A weak Harnack inequality for fractional evolution equations with discontinuous coefficients. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XII (2013), 903-940.
  25. Prüss J.; Simonett, G.; Zacher, R.: On the qualitative behaviour of incompressible two-phase flows with phase transitions: the case of equal densities . Interfaces Free Bound. 15 (2013), 405-428.
  26. Vergara, V., Zacher, R.: Optimal decay estimates for time-fractional and other nonlocal subdiffusion equations via energy methods. SIAM J. Math. Anal. 47 (2015), 210-239.
  27. Kotschote, M.; Zacher, R.: Strong solutions in the dynamical theory of compressible fluid mixtures. Math. Models Methods Appl. Sci. 25 (2015), 1217-1256.
  28. Winkert, P.; Zacher, R.: Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth. Nonlinear Anal. 145 (2016), 1-23.
  29. Kemppainen, J.; Siljander, J.; Vergara, V.; Zacher, R.: Decay estimates for time-fractional and other non-local in time subdiffusion equations in R^d. Math. Ann. 366 (2016), 941-979.
  30. Bothe, D.; Denk, R.; Hieber, M.; Schnaubelt, R.; Simonett, G.; Wilke, M., Zacher, R.:     Preface [Special issue: Parabolic evolution equations, maximal regularity, and applications—dedicated to Jan Prüss]. Bibliography: Prüss, Jan W. J. Evol. Equ. 17 (2017), 1-15.
  31. Vergara, V.; Zacher, R.: Stability, instability, and blowup for time fractional and other non-local in time semilinear subdiffusion equations. J. Evol. Equ. 17 (2017), 599-629.
  32. Kemppainen, J.; Siljander, J.; Zacher, R.: Representation of solutions and large-time behavior for fully nonlocal diffusion equations. J. Differential Equations 263 (2017), 149-201.
  33. Dier, D.; Zacher, R.: Non-autonomous maximal regularity in Hilbert spaces. J. Evol. Equ. 17 (2017), 883-907.
  34. Kemppainen, J.; Zacher, R.: Long-time behavior of non-local in time Fokker-Planck equations via the entropy method. Math. Models Methods Appl. Sci. 29 (2019), 209-235.
  35. Zacher, R.: Time fractional diffusion equations: solution concepts, regularity, and long-time behavior. Handbook of fractional calculus with applications. Vol. 2, 159–179, De Gruyter, Berlin, 2019.
  36. Spener, A.; Weber, F.; Zacher, R.: Curvature-dimension inequalities for non-local operators in the discrete setting. Calc. Var. Partial Differential Equations 58 (2019), Paper No. 171, 30pp.
  37. Spener, A.; Weber, F.; Zacher, R.: The fractional Laplacian has infinite dimension. Comm. Partial Differential Equations 45 (2020), 57-75.
  38. Dier, D.; Kemppainen, J.; Siljander, J.; Zacher, R.: On the parabolic Harnack inequality for non-local diffusion equations. Math. Z. 295 (2020), 1751–1769.
  39. Wittbold, P.; Wolejko, P.; Zacher, R.: Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equations. J. Math. Anal. Appl. 499 (2021), Paper No. 125007, 20 pp.
  40. Weber, F.; Zacher, R.: The entropy method under curvature-dimension conditions in the spirit of Bakry-Émery in the discrete setting of Markov chains. J. Funct. Anal. 281 (2021), Paper No. 109061, 81 pp.
  41. Dier, D.; Kassmann, M.; Zacher, R.: Discrete versions of the Li-Yau gradient estimate. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), 691–744.
  42. Niebel, L.; Zacher, R.: Kinetic maximal L2-regularity for the (fractional) Kolmogorov equation. J. Evol. Equ. 21 (2021), 3585–3612.
  43. Niebel, L.; Zacher, R.: Kinetic maximal Lp-regularity with temporal weights and application to quasilinear kinetic diffusion equations. J. Differential Equations 307 (2022), 29–82.
  44. Weber, F., Zacher, R.: Li–Yau inequalities for general non-local diffusion equations via reduction to the heat kernel. Math. Ann. (2022). doi.org/10.1007/s00208-021-02350-z
 
 

Preprints
 

 

  1. Kräss, S.; Weber, F.; Zacher, R.: Li-Yau and Harnack inequalities via curvature-dimension conditions for discrete long-range jump operators including the fractional discrete Laplacian. Preprint 2022, available at arxiv.org