Global existence results for first-order integrodifferential identification problems
Rendiconti del Seminario Matematico della Università di Padova, Tome 96 (1996), pp. 51-84.
@article{RSMUP_1996__96__51_0,
     author = {Lorenzi, Alfredo and Prilepko, Aleksey Ivanovic},
     title = {Global existence results for first-order integrodifferential identification problems},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {51--84},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {96},
     year = {1996},
     mrnumber = {1438288},
     zbl = {0879.45006},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_1996__96__51_0/}
}
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Lorenzi, Alfredo; Prilepko, Aleksey Ivanovic. Global existence results for first-order integrodifferential identification problems. Rendiconti del Seminario Matematico della Università di Padova, Tome 96 (1996), pp. 51-84. http://archive.numdam.org/item/RSMUP_1996__96__51_0/

[1] M. Chicco, Third boundary value problem in H2,p (Ω) for a class of linear second order elliptic partial differential equations, Rend. Ist. Mat. Univ. Trieste, 1 (1972), pp. 85-94. | Zbl

[2] G. Di Blasio, Linear parabolic equations in Lp-spaces, Ann. Mat. Pura Appl., 138 (1984), pp. 55-104. | MR | Zbl

[3] D.H. Fremlin, Topological Riesz Spaces and Measure Theory, Cambridge University Press (1974). | MR | Zbl

[4] D. Gilbarg - N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, Berlin, Heidelberg, New York (1983). | MR | Zbl

[5] P. Grisvard, Équations différentielles abstraites, Ann. Sci. Éc. Norm. Sup., 2 (1969), pp. 311-395. | Numdam | MR | Zbl

[6] V.M. Isakov, On a class of inverse problems for parabolic equations, Dokl. Akad. Nauk. SSSR, 25 (1980), pp. 519-521, (in Russian). | MR | Zbl

[7] A.D. Iskenderov, Some inverse problems for determining the right side of differential equations, Izv. Akad. Nauk. Azerb. SSSR, 2 (1976), pp. 35-44 (in Russian). | Zbl

[8] V.K. Ivanov - V.V. Vasin - V.P. Tanana, Theory of Ill-Posed Problems and its Applications, Nauka, Moscow (1977) (in Russian). | Zbl

[9] O.A. Ladyzhenskaya - V.A. Solonnikov - N.N. Ural'Ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monograph., vol 23, Amer. Math. Soc., Providence (1968). | Zbl

[10] M.M. Lavrent'Ev - V.G. Romanov - S.P. Shishatskij, Ill-Posed Problems of Mathematical Physics, Transl. Math. Monograph., vol. 64, Amer. Math. Soc., Providence (1986). | Zbl

[11] A. Lorenzi, Identification problems for integrodifferential equations, in Ill-Posed Problems in Natural Sciences, VSP (1992), pp. 342-374. | MR | Zbl

[12] A. Lorenzi - E. Paparoni, Direct and inverse problems in the theory of materials with memory, Rend. Sem. Mat. Univ. Padova, 87 (1992), pp. 105-138. | Numdam | MR | Zbl

[13] A. Lorenzi - A.I. Prilepko, Fredholm-type results for integrodifferential identification parabolic problems, Diff. Int. Eqs., 6 (1993), pp. 535-552. | MR | Zbl

[14] A. Lorenzi - E. Sinestrari, An inverse problem in the theory of materials with memory, Nonlinear Anal., 12 (1988), pp. 1317-1335. | MR | Zbl

[15] D.G. Orlovskij, The problem of determining a parameter in an evolution equation, Diff. Eqs., 26 (1990), pp. 1614-1621. | MR | Zbl

[16] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag (1983). | MR | Zbl

[17] G.N. Polozhiy, Equations of Mathematical Physics, Hayden Book Co., New York (1967).

[18] A.I. Prilepko, On inverse problems in Potential Theory, Diff. Urav., 3 (1967), pp. 30-44; English translation: Diff. Eqs., 3 (1967), pp. 14-20. | MR | Zbl

[19] A.I. Prilepko, Selected questions related to inverse problems of Mathematical Physics, in Conditionally Well-Posed Problems of Mathematical Physics and Analysis (in Russian), Nauka, Novosibirsk (1992), pp. 151-162. | MR | Zbl

[20] A.I. Prilepko - A.B. Kostin, On the identification of a coefficient in a parabolic equation I, Sib. Mat. Zh., 33 (1992), pp. 146-155. | MR | Zbl

[21] A.I. Prilepko - A.B. Kostin, On the identification of a coefficient in a parabolic equation II, Sib. Mat. Zh., 34 (1993), pp. 147-158. | MR | Zbl

[22] A.I. Prilepko - A.B. Kostin, On certain inverse problems for parabolic equations with final and integral observation, Russian Acad. Sci. Sb. Math., 75 (1993), pp. 473-490. | MR | Zbl

[23] A.I. Prilepko - A.B. Kostin - I.V. Tikhonov, Inverse problems for evolution equations, in Ill-Posed Problems in Natural Sciences, VSP (1992), pp. 379-389. | MR | Zbl

[24] A.I. Prilepko - D.G. Orlovskij - I.A. Vasin, Inverse problems in Mathematical Physics, in Ill-Posed Problems in Natural Sciences, VSP (1992), pp. 390-407. | MR | Zbl

[25] A.I. Prilepko - V.V. Solovyev, Solvability theorems and Rothe's method for inverse problems for an equation of parabolic type, Diff. Eqs., 23 (1987), pp. 1971-1980. | MR | Zbl

[26] A.I. Prilepko - I.V. Tikhonov, Uniqueness of the solution to an inverse problem related to an evolution equation and applications to the transfer equation, Mat. Zam., 51 (1992), pp. 77-88. | MR | Zbl

[27] A.I. Prilepko - I.V. Tikhonov, Inverse problems with final determination related to abstract evolution equations in ordered Banach spaces, Funct. Anal. Pri., 27 (1993), pp. 81-83. | MR | Zbl

[28] A.I. Prilepko - I.V. Tikhonov, Determination of a homogeneous addend in abstract inverse problems, Izv. R.A.N. Mathematical Series, 58 (1994), pp. 167-188. | MR | Zbl

[29] A.I. Prilepko - I.A. Vasin, Inverse initial boundary value problems for linearized nonstationary Navier-Stokes equations, Diff. Eqs., 25 (1989), pp. 106-117. | MR | Zbl

[30] A.I. Prilepko - I.A. Vasin, Inverse initial boundary value problems for nonlinear Navier-Stokes equations, Diff. Eqs., 25 (1989), pp. 2164-2177. | MR | Zbl

[31] A. Rundell, Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data, Appl. Anal., 10 (1980), pp. 231-242. | MR | Zbl

[32] V.V. Solovyev, Fredholmness in an inverse problem related to the determination of the free member in a parabolic equation in Analysis of Mathematical Models of Physical Processes, Energoatomizdat Moscow (1988), pp. 90-95.

[33] H. Tanabe, Equations of Evolution, Pitman, London (1979). | MR | Zbl

[34] A.N. Tikhonov - V. Ya. ARSENIN, Méthodes de résolution des problèmes mal posés, Mir, Moscow (1973).

[35] K. Yosida, Functional Analysis, Springer-Verlag, Berlin (1968).