Boundary-value Problems with Non-local Initial Condition for Parabolic Equations with Parameter


  • John Michael Rassias Professor, Pedagogical department, Mathematics and Informatics section, National and Capodostrian University of Athens
  • Erkinjon Tulkinovich Karimov Senior researcher of the Institute of Mathematics and Inofrmation Technologies, Uzbek Academy of Sciences


Degenerate parabolic equation, forward-backward parabolic equation with a parameter, boundary-value problems with non-local initial conditions, classical "a-b-c" method.


In 2002, J.M.Rassias (Uniqueness of quasi-regular solutions for bi-parabolic elliptic bi-hyperbolic Tricomi problem, Complex Variables, 47 (8) (2002), 707-718) imposed and investigated the bi-parabolic elliptic bi-hyperbolic mixed type partial differential equation of second order. In the present paper some boundary-value problems with non-local initial condition for model and degenerate parabolic equations with parameter were considered. Also uniqueness theorems are proved and non-trivial solutions of certain non-local problems for forward-backward parabolic equation with parameter are investigated at specific values of this parameter by employing the classical "a-b-c" method. Classical references in this field of mixed type partial differential equations are given by: J.M.Rassias (Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, 1990, pp.1-144) and M.M.Smirnov (Equations of Mixed Type, Translations of Mathematical Monographies, 51, American Mathematical Society, Providence, R.I., 1978 pp.1-232). Other investigations are achieved by G.C.Wen et al. (in period 1990-2007).






Special Issue on Complex Analysis: Theory and Applications

How to Cite

Boundary-value Problems with Non-local Initial Condition for Parabolic Equations with Parameter. (2010). European Journal of Pure and Applied Mathematics, 3(6), 948-957.