“I keep the subject constantly before me and wait until the first dawnings open slowly, by little and little, into a full and clear light” (Isaac Newton)
Graduated from Faculty of Mechanics and Mathematics of Donetsk National University.
Postgraduate student at the Institute of Applied Mathematics and Mechanics of NAS of Ukraine.
Candidate thesis on “Topological methods in the theory of nonlinear boundary value problems” was presented.
Junior researcher of the Institute of Applied Mathematics and Mechanics of NAS of Ukraine.
Senior researcher of the Institute of Applied Mathematics and Mechanics of NAS of Ukraine.
Doctoral thesis on “Saint-Venant’s principle and its applications in the qualitative theory of nonlinear boundary value problems” was presented.
Leading researcher in the Department of partial differential equations of the Institute of applied mathematics and mechanics of NAS of Ukraine.
Head of the Department of partial differential equations of the Institute of Applied Mathematics and Mechanics of NAS of Ukraine.
Head of the Scientific Center of Nonlinear Problems of Mathematical Physics of S.M. Nikol’skii Mathematical Institute of RUDN University.
A.E. Shishkov delivered lectures on the following topics at Donetsk National University:
- Partial differential equations;
- Ordinary differential equation;
- Functional analysis;
- Topological methods and functional analysis methods for nonlinear boundary value problems;
- Qualitative theory of nonlinear elliptic and parabolic equations.
- 1987 - Mathematical Institute of Czechoslovak Academy of Sciences, Prague, Czechoslovakia;
- 1989 - Weierstass Institute, Berlin, Germany;
- 1994 - 1995 - Computer and Automation Institute (CAI) of Hungarian Academy of Sciences, Budapest, Hungary;
- 1995 – 1996 - Catania University, Italy;
- 1996 - Leiden University, the Netherlands; University of Besancon, France;
- 1997 - Instituto per le Applicazioni del Calcolo (IAC) “Mauro Picone”, Rome, Italy; University of Twente, the Netherlands; (University of Leiden, the Netherlands; Mathematical Institute of Wroclaw University, Poland;
- 1999 - University of Rome “La Sapienza”, Rome, Italy; University of Toulouse Paul Sabatier, Toulouse, France; University of Bath, England;
- 2001 – 2002 - University of Roma “La Sapienza”, University of Bath, UK; CAI of Hungarian Academy of Sciences, Budapest, Hungary; Israel Institute of Technology (Technion), Haifa, Israel.
- 2003 - University of Roma “La Sapienza”, University of Bath, UK.
- 2004 - University of Tours, France; University of Bath, UK.
- 2005 - Technion, Haifa, Israel; University of Bath, UK.
- January - February 2006 - University of Bath, UK.
- June - July 2006 - University of Tours, France; Humboldt University and Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany.
- March – October 2007 - University of Tours, France; University of Bath, UK; University of Swansea, UK; University Technion, Haifa, Israel.
- September - December 2008 - University of Tours, France; Israel Institute of Technology (Technion), Haifa, Israel.
- October - November 2010, October 2011, November 2013, March 2015 - visiting professor, University of Tours, France.
- February - March 2011, January 2012, February 2013, November 2014, January 2018 - visiting professor Israel Institute of Technology (Technion), Haifa, Israel.
Member of the editorial boards of the journals:
- Ukrainian mathematical bulletin;
- Ukrainian mathematical journal;
- Abstract and Applied Analysis.
- A number of variants of the method of local energy evaluation in the qualitative theory of nonlinear boundary value problems, which allowed to establish a number of fundamental results on the asymptotic and qualitative properties of generalized solutions of broad classes of quasi-linear elliptic, parabolic and some composite classes of differential equations was developed.
- Local variants of energy and entropy a priori evaluations of generalized solutions of the flow equations of thin viscous films, specific quasilinear parabolic equations of the fourth order were obtained in 1995. On the basis of these evaluations terms of finiteness of speed of distribution of carriers of the corresponding decisions were define in a number of works, and also the description of various scenarios of evolution of these carriers in time was given.
- A new energy method for studying linear parabolic boundary value problems with infinitely aggravating (growing) finite-time boundary value data was proposed in 1999. On the basis of this method, the exact classes of localized boundary modes (S-modes), that is, modes with exacerbation, generating solutions with spatially localized at the time of exacerbation of the singularity zone were described.
- Exact terms on the nature of the degeneracy capacity (Dini type terms) to ensure the absence of propagation of singularities of solutions and, consequently, the existence supersingular and “large” solutions were set together with professor L. Veron. It was proved with professor M. Marcus that on a wide class of potentials the Dini term is a necessary condition for the absence of singularity propagation along degeneracy varieties, that is, the criterion for the existence of these classes of singular solutions was found.
- Qualitative theory of solutions of boundary value problems for quasilinear and nonlinear elliptic and parabolic equations of the second and high orders;
- Equation of flow of thin capillary films;
- Cahn-Hilliard equation;
- Theory of singular, super-singular and “large” solutions of nonlinear diffusion-absorption structure equations;
- Localized and non-localized boundary regimes with singular exacerbation.