Pliska Studia Mathematica Bulgarica

Volume 23, 2014



C O N T E N T S


A B S T R A C T S


BERNSTEIN INEQUALITY FOR 1 − D HAMILTONIANS WITHOUT RESONANCES
Vladimir Georgiev georgiev@dm.unipi.it,
Anna Rita Giammetta giammetta@mail.dm.unipi.it

2010 Mathematics Subject Classification: 35P05, 42B25, 46E25, 42B15.
Key words: Bernstein inequality, Hamiltonians with potential, Sobolev spaces, Besov spaces.


EXPLICIT FORMULAS TO THE SOLUTIONS OF SEVERAL EQUATIONS OF MATHEMATICAL PHYSICS
Petar Popivanov popivano@math.bas.bg

2010 Mathematics Subject Classification: 35C05, 35L05, 35Q53, 35S10.
Key words: Klein-Gordon equation, wave equation, semilinear hyperbolic equation, Kadomtsev-Petviashvili equation, solution into closed form.


3D MODELLING OF WAVE PROPAGATION IN SOLID MEDIA AND APPLICATIONS IN GEOPHYSICS
Georgi Boyadzhiev gpb@math.bas.bg

2010 Mathematics Subject Classification: 35L53, 35Q86, 86A15.
Key words: key words Strongly coupled linear hyperbolic systems, modelling of multi-layered solid body, applications in Geophysics.


EXISTENCE RESULTS FOR SOME VARIATIONAL INEQUALITIES INVOLVING NON-NEGATIVE, NON-COERCITIVE BILINEAR FORMS
Georgi Chobanov chobanov@math.bas.bg

2010 Mathematics Subject Classification: 35J85.
Key words: variational inequalities, semi-coercive bilinear forms, recession cone.


NUMERICAL METHODS FOR DELAYED DIFFERENTIAL EQUATIONS WITH DISCONTINUITES
T. Donchev tzankodd@gmail.com,
D. Kolev kolev@mmu.uctm.edu, kolev@uctm.edu
A. Nosheen hafiza@gmail.com,
M. Rapaqat m.rafaqat50@gmail.com,
A. Zeinev a_zejnev@uctm.edu

2010 Mathematics Subject Classification: 34A37.
Key words: Impulsive differential equations, Runge-Kutta methods, delay.


SHARP HARDY INEQUALITIES IN A BALL
Alexander Fabricant,
Nikolai Kutev,
Tsviatko Rangelov rangelov@math.bas.bg

2010 Mathematics Subject Classification: 26D10.
Key words: Hardy inequality, sharp estimates.


GLOBAL BEHAVIOR OF THE SOLUTIONS TO SIXTH ORDER BOUSSINESQ EQUATION WITH LINEAR RESTORING FORCE
N. Kutev,
N. Kolkovska natali@math.bas.bg,
M. Dimova mkoleva@math.bas.bg

2010 Mathematics Subject Classification: 35L30, 76B15, 65M06.
Key words: Sixth order Boussinesq equation, potential well method, finite time blow up, arbitrary high positive initial energy.


ON THE REGULARITY PROPERTIES OF THE PRESSURE FIELD ASSOCIATED TO A HOPF WEAK SOLUTION TO THE NAVIER-STOKES EQUATIONS
Jmmy Alfonso Mauro jmmyamauro@math.bas.bg

2010 Mathematics Subject Classification: 76D05, 35Q30, 76D03.
Key words: Navier-Stokes equations, Leray-Hopf weak solutions, regularity of the pressure field.


SPECTRAL FINITE DIFFERENCE ANALYSIS OF NATURAL CONVECTION IN A TWO-DIMENSIONAL ENCLOSURE OF A THREE-FINS TYPE
Yoshihiro Mochimaru

2010 Mathematics Subject Classification: 30C20, 65N06, 76R10.
Key words: spectral analysis, natural convection, finite difference.


ANTI-PLANE SCATTERING BY HETEROGENEITIES IN PIEZOELECTRIC PLANE BY BIEM
Tsviatko Rangelov rangelov@math.bas.bg,
Petia Dineva petia@imbm.bas.bg

2010 Mathematics Subject Classification: 74J20, 74S15, 74G70.
Key words: MDL, multifunctional nano-structured materials, electro-mechanical dynamic load, integro-differential equations, boundary integral equation method.


PROGRAMME PACKAGES FOR IMPLEMENTATION OF MODIFICATIONS OF BLACK-SCHOLES MODEL AND WEB APPLICATIONS
Angela Slavova slavova@math.bas.bg,
Nikolay Kyurkchiev nkyurk@math.bas.bg

2010 Mathematics Subject Classification: 65M12, 65Y20.
Key words: Black-Scholes model, market price, coefficient of variation, Garman-Kohlhagen model, programming environment MATHEMATICA.


APPLICATIONS OF EQUATIONS OF MATHEMATICAL PHYSICS IN STUDYING TSUNAMI WAVES
Angela Slavova slavova@math.bas.bg,
Pietro Zecca zecca@unifi.it

2010 Mathematics Subject Classification: 76B15, 35Q80, 92B20.
Key words: Tsunami waves, equations of mathematical physics, viscoelastic Burgers equation, Cellular Nonlinear Networks, traveling wave solution, generalizations.


2D FRACTURE PROBLEMS IN MAGNETO-ELECTRO-ELASTIC COMPOSITE MATERIALS UNDER ANTI-PLANE WAVES BY BIEM
Yonko Stoynov jds@tu-sofia.bg


ON THE INSTABILITY OF ACTION VARIABLES IN NON-CONVEX HAMILTONIAN SYSTEMS
Borislav Yordanov byordanov@math.bas.bg,
Roumyana Yordanova ryordanova@math.bas.bg

2010 Mathematics Subject Classification: Primary 37J25, 37J40; Secondary 37C10, 37C40.
Key words: Hamiltonian systems, instability, resonances, Arnold diffusion.