RESEARCH FIELDS:

 

PUBLICATION and PhD Students

PhD Students

 

1. K. Ianakiev

2. N. Tzvetkov, (Permanent position CNRS, Orsay, Paris, France and Ass. professor Univ. of Lille)

3. S. Lucente (Permanent position Univ. of Potenza)

4. B.Iordanov

5. R. Kirova

6. K.Azgorov

7. F. Catalano

8. S. Di Pomponio

9. G. Venkov (Permanent position Technical University,Sofia)

10. N.Visciglia ( Assistantship Position University of Pisa)

11. S. Zappacosta

12. A.Ivanov

13. M.Tarulli

14. D.Catania

15. J.Mauro

 

link to

Arxive preprint page

PUBLICATIONS:

[1] Inverse scattering problem for symmetric strictly hyprbolic systems, Compt. Rend. Acad.
Bulg. Sci. 35(5), 1982, 593 - 596.
[2] Disappearing solutions of symmetric strictly hyperbolic systems, Compt. Rend. Acad.
Bulg. Sci. 36(2), 1983, 323 - 324.
[3] A uniqueness theorem of Holmgren's type for first order systems, Compt. Rend. Acad.
Bulg. Sci. 37(6), 1984, 733 - 736.
[4] Construction of smooth basis depending on a parameter, Higher School Appl.Math. 20(2),
1984, 27 - 30 (with Ja. Arnaoudov).
[5] Construction of a real analytic basis for matrices with real analytic elements, Higher
School Appl. Math. 20(2), 1984, 32 - 35 (with Ja. Arnaoudov).
[6] Wave fronts of solutions to boundary problems for symmetric dissipative systems, Serdica,
10, 1984, 41 - 48.
[7] Existence and completeness of the wave operators fot dissipative hyperbolic systems of
constant multiplicity, Compt. Rend. Acad. Bulg. Sci. 38(6), 1985, 667 - 670.
[8] High frequency asymptotics of the filterred scattering amplitudes and the inverse scattering
problem for dissipative hyperbolic systems, I part, Math. Nachr., 117, 1985, 111 - 128, II
part, Math. Nachr., 122, 1985, 267 - 275.
[9] The Kreiss condition for disipative hyperbolic systems of constant multiplicity, Boll. Un.
Math. It., (6) 3 - B, 1984, 383 - 395.
[10] Controllability of the scattering operator for dissipative hyperbolic systems, Math.
Nachr., 122, 1985, 339 - 346.
[11] Interior solution of Einstein's equations for hydrogen atom, Diff. eq. and applications,
Ruse 1985, p. 635 - 638, Angel Kanchev Tech. Univ, Ruse 1987.
[12] Existence and completeness of the wave operators for dissipative hyperbolic systems, J.
Operator Theory, 14, 1985, 291 - 310.
[13] Disappearing solutions for dissipative hyperbolic systems of constant multiplicity, Hokkaido
Math. J., 15(3), 1986, 357 - 385.
[14] Existence of the scattering operator for dissipative hyperbolic systems with variable
multiplicity, J. Operator Theory, 19, 1988, 217 - 241 (with P. Stefanov).
[15] Leading singularity of the scattering kernel for the Maxwell equations outside moving
obstacles, Compt. Rend. Acad. Bulg. Sci. 41(10), 1988, 17 - 20.
[16] Global existence of solution to the semilinear heat equation, Compt. Rend. Acad. Bulg.
Sci., 42(6), 1989, 21 - 24.(with M.Marinov)
[17] Global solution to the Maxwell - Dirac equations, Compt. Rend. Acad. Bulg. Sci.,
42(6), 1989, 17-20.
[18] Leading term of the solution to the Klein - Gordon equation, Compt. Rend. Acad.
Bulg. Sci., 42(12), 1989, 25 - 28.
[19] A weighted estimate of the solution to the wave equation, Compt. Rend. Acad. Sci.
Bulg. 42(11), 1989, 17 - 20 (with V.Covachev).
[20] Theoreme de type RAGE pour des ope'rateurs a' puissances bornees, Compt. Rend.
Acad. Sci. Paris, 303, Se'rie I, No. 13, 1986, 605 - 608 (with V.Petkov).
[21] Local energy decay for the wave equation and hyperbolic systems, Publ. of Patras Univ.,
Patras, 1986, 31 - 54.
[22] Inverse scattering problem for the Maxwell equations outside moving body, Ann. Inst.
H.Poincare', (Physique The'orique), 50(1), 1988, 1 - 34.
[23] RAGE theorem for power bounded operators and local energy decay for moving obstacles,
Ann. Inst. H.Poincare', (Physique The'orique), 51(2), 1989, 155 -185 (with V.Petkov).
[24] Inverse scattering problem for dissipative wave equation, Integral equations and inverse
problems (Varna, 1989) p.86 - 89, (Pitman Res. Notes Math. Ser.) v. 235 , Longman Sci.
Tech. Harlow, 1992.
[25] Global solution of the system of wave and Klein - Gordon equations, Math. Zeit. 203,
1990, 683 - 698.
[26] L'existence des solutions globales pour des syst`emes nonline'aires avec champs massifs
et sans masse, Compt. Rend. Acad. Sci. Paris, Se'rie I, 308, 1989, 529 - 532.
[27] Existence des solutions globales pour le syst`eme de Maxwell-Dirac, Compt. Rend. Acad.
Sci. Paris, Se'rie I, 310, 1990, 569 - 572.
[28] Gauge invariant Maxwell-Dirac equations and their global solutions, Comp. Rend. Acad.
Bulg. Sci., 43(9), 1990, 17 - 20 (with E. Evtimova).
[29] Weighted decay estimates for the wave equation, Proc. Amer. Math. Soc., 112, 1991 ,
393 - 402 (with V.Covachev).
[30] A counterpart of the Poincare' group for pseudodifferential
operators,
Acad. Bulg. Sci., 44(2), 1991, 17 - 20 (with V.Covachev)
[31] Global solutions to the nonlinear equaions in relativistic quantum mechanics , Surveys
on Geometry, Analysis and Math. Physics, 1990, Band 17, 54 - 138, Teubner Text, Berlin (with
V. Covachev).
[32] Inverse scattering problem for dissipative wave equation, Mat. Aplicada e Comp., 9(1),
1990, p. 59 - 78 (with Ja. Arnaoudov).
[33] Global solutions to the two dimensional Klein - Gordon equation, Compt. Rend. Acad.
Sci. Paris, Se'rie I, 311, 1990, 87 - 90.(with P. Popivanov)
[34] Existence of global solution of a nonlinear wave equation with short-range potential,
Part. Diff. Equations, Part 1,2 Warsaw 1990, Banach Center Publ. 27, Part 1, v. 2, p. 163 -
167, Polish Acad. Sci., Warsaw.
[35] Global solution to the two dimensional Klein - Gordon equation, Comm. Part. Diff.
Eq.,16 (6,7) 1991, 941 - 995 (with P.Popivanov).
[36] Small amplitude solutions of the Maxwell - Dirac equations, Indiana Univ. Math.
Journal, 40 (3) 1991, 845 - 883.
[37] Existence of solution of the wave equation with nonlinear damping and source terms,
C.R.Acad. Sci. Paris, t.314, Ser. I, 1992, 205 - 209. (with. G.Todorova)
[38] Developing the solution of Stefan’s problem, C.R.Acad. Sci. Bulg. 47 (1994)No. 3 p.
9-12 ( with S.Bushev)
[39] The asymptotic behaviour of Yang - Mills fields in the large, Preprint No. 170 of
Rheinische - Friedrich - Wilhelms - Univ, 1991 and Comm. Math. Phys. 148, 1992, 425 - 444
(with P.Schirmer).
[40] Decay estimates for the Klein - Gordon equation, Comm. Part. Diff. Eq. 17( 7 and 8),
1992, 1111 - 1139.
[41] Critical point of the "entropy" - like functional for the quantum distribution functions,
Helv. Phys. Acta, 65, 1992, 596 - 610. (with. E.Evtimova)
[42] Numerical algorithm for the dynamic analysis of base-isolated structures with dry friction,
Natural Hazards, 6, 1992, 71 - 86, (with S.Dimova).
[43] A method for generating exact solutions of the nonlinear Klein-Gordon equation, Canad.
J. Phys. 70 (1992) No. 6 , p. 467 - 469 (with A.Grigorov, N.Martinov, D Orushev)
[44] High-frequency asymptotics in inverse scattering by ellipsoids, Math. Meth. in Appl.
Sciences, 16, 1993, 1-12 (with Y. Arnaoudov, G.Dassios)
[45] Existence of solution of the wave equation with nonlinear damping and source terms,
Journal Diff. Equations 109(2), 1994, 295 - 308. (with. G.Todorova).
[46] Global existence of low regularity solutions of non-linear wave equations, Math. Zeitschrift,219,
1995, p.1-19. (with P.P.Schirmer)
[47] Space time estimates for compatible forms associated with first order hyperbolic systems,
Compt. Rend. Acad. Sci. Paris, 318, Serie I, 1994, 1109 - 1114.(with P.Schirmer)
[48] Solitary solutions of the Maxwell-Dirac and Klein-Gordon-Dirac equations, preprint
CEREMADE 9514(1995) and Calculus of Variations and Part. Diff. Eq. 4, 1996, p.265-281.(con
M.Esteban, E.Sere)
[49] Solitary-wave solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac systems,
preprint CEREMADE 9524(1995) and Letters Math. Phys 1996, v.38(2) p.217-220 .(con M.Esteban,
E.Sere)
[50] Weighted decay estimates for the wave equation, Comp. Rend. Acad. Sci. Paris,t.322,
1996, p. 829-834.
[51] Existence of global solutions to supercritical semilinear wave quations, Serdica, 22,
1996, 2, p. 125 - 164.
[52] Weighted Strichartz estimates and global existence for semilinear wave equation, Amer.
J. Math. vol. 119(6), 1997, p.1291-1319. (with H.Linblad and C. Sogge)
[53] Global existence of solutions and formation of singularities for a class of hyperbolic
systems, Geometric optics and related topics, F.Colombini, N.Lerner, Ed, Progress in Nonlinear
Differential Equations and Their Applications, 1997, p.117-140.
[54] Weighted estimate for the wave equation, Gakuto Int. Series, Mathematical Sciences
and Applications, vol.10 (1997), 75-83.
[55] On the asymptotic behaviour of semilinear wave equations with degenerate dissipation
and source terms, Preprint ICTP IC/96/96, 1996. NoDEA Nonlinear Diff. Equations Appl.
1998, 5(1) p. 53-68 (con A.Milani)
[56] Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation Compt. Rend.
Acad. Sci. Paris, 1999 (con S.Lucente)t. 329, Serie I, p.21-26.
[57] P.D'Ancona, V.Georgiev, H.Kubo, Weighted decay estimates for the wave equation and
low regularity solutions, Rendiconti dell'Ist. Mat. dell'Univ. Trieste vol 31, 2000, supl. 2,
p.51-62.
[58] V.Georgiev, C.Heiming, H.Kubo, Critical exponent for wave equation with potential,
Rendiconti dell'Ist. Mat. dell'Univ. Trieste vol 31, 2000, supl. 2, p.103-128.
[59] V.Georgiev, S. Di Pomponio, Life-span of subcritical semilinear wave equation, Asymptotic
Analysis, : Volume 28, 2,2001, p. 91 - 114.
[60] C.Heimig, V.Georgiev, H.Kubo, Supercritical semilinear wave equation witn non-negative
potential, Comm. Part. Diff. Equations , V. 26 , Issue 11,12, 2001.
[61] P.D'Ancona, V.Georgiev, H.Kubo, Weighted decay estimates for the wave equation,
Journal Diff. Equations, Vol. 177, No. 1, November 20, 2001, p. 146-208
[62] V.Georgiev, Nonlinear hyperbolic equations in mathematical physics, Japanese Math.
Society, 2000, 255p.
[63] V.Georgiev, S. Di Pomponio, Lower bound for the life - span of higher dimensional wave
equation, Compt. Rend. Acad. Bulg. Sci. 2001, v. 54, No. 3, 11-14.
[64] V.Georgiev and P. D'Ancona , On Lipschitz continuity of the solution map for twodimensional
wave maps, Banach Center Publ. 2003, vol. 60, p. 95 - 103. EVOLUTION
EQUATIONS Propagation Phenomena - Global Existence - Influence of Non-Linearities, Rainer
Picard, Michael Reissig, Wojciech Zajaczkowski (eds.) Warszawa 2003
[65] V.Georgiev, N.Visciglia, Dispersive estimates for the wave equation with potential, Rendiconti
Lincei Matematica e Applicazioni, 2003, v. 14, s. 9 p. 109 - 135.
[66] V.Georgiev , N.Visciglia, Decay estimates for the wave equation with potential, Comm.
Part. Diff. Eq. vol.28 No. 7,8 (2003) p. 1325 - 1369.
[67] D'Ancona, Piero; Georgiev, Vladimir Recent ill-posedness results for the wave map
system in critical spaces. Hyperbolic problems and related topics, 137-146, Grad. Ser. Anal.,
Int. Press, Somerville, MA, 2003.
[68] V.Georgiev, Sandra Lucente, Decay for nonlinear Klein - Gordon equations, NoDEA,
2004, Volume 11, Number 4, 529 - 555
[69] Vladimir Georgiev, Sandra Lucente, Guido Ziliotti, Decay estimates for hyperbolic systems,
Hokkaido Math. Journal 2004, vol. 33, p.83-113.
[70] V.Georgiev, P.D'Ancona, Low regularity solutions for the wave map equation into the
2-D sphere, Math. Zetschrift, Volume 248, Number 2 ( 2004) p. 227-266 .
[71] V.Georgiev, P.D'Ancona, On the continuity of the solution operator to the wave map
system, CPAM. 57 (2004), no. 3, 357-383.
[72] V.Georgiev, G.M. Coclite, Solitary waves for Maxwell -
Schroedinger equations, Electron.
J. Differential Equations 2004, No. 94, 1 - 31 pp. (electronic).
[73] V.Georgiev, A.Ivanov, Concentration of local energy for two-dimensional wave maps,
Rend. Istit. Mat. Univ. Trieste, vol. 35, p.195-235 (2003)
[74] Georgiev, Vladimir; Karadzhov, Georgi; Visciglia, Nicola Endpoint Strichartz estimates
for the wave equation in the critical case. Phase space analysis of partial differential equations.
Vol. I, 225-233, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004.
[75] D.Catania, V.Georgiev, Semilinear wave equation in Schwarzschild metric. Nuovo Cimento
Soc. Ital. Fis. B 119 (2004), no. 7-9, 661-683.
[76] V.Georgiev, B.Rubino, R.Sampalmieri, Global existence for elastic waves with memory,
Arcive Rat. Mech. Anal. 176 (2005) p.303-330.
[77] Georgiev, Vladimir; Visciglia, Nicola Solitary waves for Klein-Gordon-Maxwell system
with external Coulomb potential. J. Math. Pures Appl. (9) 84 (2005), no. 7, 957-983.
[78] V.Georgiev, A.Ivanov, Existence and mapping properties of wave operator for the
Schr¨odinger equation with singular potential Proc. Amer. Math. Soc. 133 (2005), 1993-2003.
[79] Georgiev, Vladimir, Semilinear hyperbolic equations. With a preface by Y. Shibata.
Second edition. MSJ Memoirs, 7 (2nd ed.). Mathematical Society of Japan, Tokyo, 2005, 209 pp.
[80] Catania, D.; Georgiev, V. Large time behaviour of solutions to the semilinear wave
equation in Schwarzschild metric. C. R. Acad. Bulgare Sci. 58 (2005), no. 6, 623-628.
[81] V.Georgiev, H.Takamura, Zhou Yi, The lifespan of solutions to nonlinear systems of
high dimensional wave equation, Nonlinear Analysis 64 (2006) 2215 - 2250.
[82] Scale invariant energy smoothing estimates for the Schroedinger Equation with small
Magnetic Potential Authors: Vladimir Georgiev, Mirko Tarulli, Asymptotic Analysis, 47 (2006)
107 -138.
[83] Davide Catania, Vladimir Georgiev, Blow Up for the Semilinear Wave Equation in
Schwarzschild Metric, Diff. Int. Equations, vol.19(7) 2006 p. 799 - 830.
[84] V.Georgiev, P. D'Ancona, Dispersive Nonlinear Problems in Mathematical Physiscs,
Quaderni di Matematica, vol. 15, 2005.
[85] V.Georgiev, A.Stefanov, Smoothing - Strichartz Estimates for the Schrodinger Equation
with small Magnetic Potential Authors: Vladimir Georgiev, Atanas Stefanov, Mirko Tarulli,
Discrete and Continuous Dynamical Systems 2007, A18, p.159 - 186.
[86] V.Georgiev, I.Arnaoudov, J.Venkov, Does Atkinson - Wilcox converges for any convex
domain, Serdica, 2007, 33, 363-376
[87] V.Georgiev, R.Kirova, B.Rubino, R.Sampalmieri, B.Yordanov, Asymptotic behaviour
for linear and nonlinear elastic waves for materials with memory, Journal of non - crystalline
solids, 354 (2008) 4126 - 4137
[88] Georgiev, V.; Visciglia, N. About resonances for Schrdinger operators with short range
singular perturbation. Topics in contemporary differential geometry, complex analysis and mathematical
physics, 74-84, World Sci. Publ., Hackensack, NJ, 2007.
[89] Georgiev Vladimir, Sandra Lucente, Nonlinear multiplicative inequalities in Sobolev
spaces associated with Lie algebras, Nonlinear Analysis Series A: Theory, Methods and Applications
Nonlinear Analysis: Volume 70, Issue 4, 15 February 2009, Pages 1574-1609.
[90] V. Georgiev, J. A.Mauro, G. Venkov, Spectral Properties of an Operator Associated with
Hartree Type Equations with External Coulomb Potential, Rendiconti dell'Istituto di Matematica
dell'Universita' di Trieste vol. 42 Suppl. (2010) p.51 - 66.
[91] Georgiev Vladimir, George Venkov, Existence of wave operators for Hartree type equations,
preprint 2008.