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

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Abstract (2. Language): 
In 2002, J.M.Rassias [14] 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 [16] and M.M.Smirnov [25]. Other investigations are achieved by G.C.Wen et al. (in period 1990-2007).
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REFERENCES

References: 

[1] A.S.Berdyshev and E.T.Karimov. Some non-local problems for the parabolic-hyperbolic
type equation with non-characteristic line of changing type. CEJM, 4(2): 183-193, 2006.
[2] F.I.Frankl. On the problems of Chaplygin for mixed subsonic and supersonic flows.
Izv.Akad. Nauk SSSR Ser. Mat., 9:121-143, 1945.
[3] A.Friedman. Fundamental solutions for degenerate parabolic equations. Acta Mathemat-
ica, 133:171-217, 1975.
[4] M.Gevrey. Sur les equations aux derivees partielles du type parabolique. J.Math.Appl.,
4:105-137, 1914.
[5] Yu.P.Gorkov. Construction of a fundamental solution of parabolic equation with degeneration.
Calcul. methods and programming, 6:66-70, 2005.
[6] A.Hasanov. Fundamental solutions of generalized bi-axially symmetric Helmholtz equation.
Complex Variables and Elliptic Equations, 52(8):673-683, 2007.
[7] S.Huang, Y.Y.Qiao and G.C.Wen. Real and complex Clifford analysis. Advances in Complex
Analysis and its Applications, 5. Springer, New York, 2006.
[8] N.I.Ionkin. The stability of a problem in the theory of heat condition with non-classical
boundary conditions. (Russian). Differencial’nye Uravnenija, 15(7):1279-1283, 1979.
[9] N.I.Ionkin and E.I.Moiseev. A problem for a heat equation with two-point boundary
conditions. (Russian). Differencial’nye Uravnenija 15(7):1284-1295, 1979.
[10] E.T.Karimov. About the Tricomi problem for the mixed parabolic-hyperbolic type
equation with complex spectral parameter. Complex Variables and Elliptic Equations,
56(6):433-440, 2005.
[11] E.T.Karimov. Some non-local problems for the parabolic-hyperbolic type equation with
complex spectral parameter. Mathematische Nachrichten, 281(7):959-970, 2008.
[12] A.A.Kerefov. The Gevrey problem for a certain mixed-parabolic equation. (Russian) Dif-
ferencial’nye Uravnenija ,13(1):76˝U83, 1977.
[13] C.D.Pagani and G.Talenti. On a forward-backward parabolic equation. Annali di Matem-
atica Pura ed Applicata, 90(1):1-57, 1971.
[14] J.M.Rassias. Uniqueness of Quasi-Regular Solutions for a Bi-Parabolic Elliptic Bi-
Hyperbolic Tricomi Problem. Complex Variables and Elliptic Equations, 47(8):707-718,
2002.
[15] J.M.Rassias. Mixed Type Partial Differential Equations in Rn, Ph.D. Thesis, University of
California, Berkeley, USA, 1977.
[16] J.M.Rassias. Lecture Notes on Mixed Type Partial Differential Equations. World Scientific,
1990.
[17] J.M.Rassias. Mixed type partial differential equations with initial and boundary values
in fluid mechanics. Int.J.Appl.Math.Stat., 13(J08):77-107, 2008.
[18] J.M.Rassias, A.Hasanov. Fundamental solutions of two degenerated elliptic equations
and solutions of boundary value problems in infinite area. Int.J.Appl.Math.Stat.,
8(M07):87-95, 2007.
[19] J.M.Rassias. Tricomi-Protter problem of nD mixed type equations. Int.J.Appl.Math.Stat.
8(M07):76-86, 2007.
[20] J.M.Rassias. Existence of weak solutions for a parabolic elliptic-hyperbolic Tricomi problem.
Tsukuba J.Math., 23(1):37-54, 1999.
[21] J.M.Rassias. Uniqueness of quasi-regular solutions for a parabolic elliptic-hyperbolic Tricomi
problem. Bull.Inst.Math.Acad.Sinica, 25(4):277-287, 1997.
[22] K.B.Sabitov. To the theory of mixed parabolic-hyperbolic type equations with spectral
parameter. Differencial’nye Uravnenija, 25(1):117-126, 1989.
[23] N.N.Shopolov. Mixed problem with non-local initial condition for a heat conduction
equation. Reports of Bulgarian Academy of Sciences, 3(7):935-936, 1981.
[24] M.M.Smirnov. Degenerate elliptic and hyperbolic equations. Nauka, Moscow, 1966.
[25] M.M.Smirnov Equations of Mixed Type, Translations of Mathematical Monographies,
51, American Mathematical Society, Providence, R.I. pp.1-232. 1978.
[26] G.C.Wen. The Exterior Tricomi Problem for Generalized Mixed Equations with Parabolic
Degeneracy. Acta Mathematics Sinica, English Series, 22(5):1385-1398, 2006.
[27] G.C.Wen and D.Chen. Discontinuous Riemann-Hilbert problems for quasilinear degenerate
elliptic complex equations of first order. Complex Variables and Elliptic Equations
50(7-11):707-718, 2005.
[28] G.C.Wen. The mixed boundary-value problem for second order elliptic equations
with degenerate curve on the sides of an angle. Mathematische Nachrichten, 279(13-
14):1602-1613, 2006.
[29] G.C.Wen and H.G.W.Begehr. Boundary value problems for elliptic equations and systems.
Pitman Monographs and Surveys in Pure and Applied Mathematics, 46. Longman Scientific
and Tech., Harlow; John Wiley and Sons, Inc.,N.Y., 1990.

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