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## Banach Center Publications

1992 | 27 | 1 | 101-109
Tytuł artykułu

### $L_p$-theory of boundary value problems for Sobolev type equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
101-109
Opis fizyczny
Daty
wydano
1992
Twórcy
autor
• Institute of Mathematics, Russian Academy of Sciences, Universitetskiĭ, Prosp. 4, 630090 Novosibirsk, Russia
Bibliografia
• [1] G. I. Barenblatt, J. P. Zheltov and I. N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech. 24 (1960), 1286-1303.
• [2] P. I. Chen and M. E. Gurtin, On a theory of heat conduction involving two temperatures, Z. Angew. Math. Phys. 19 (1968), 614-627.
• [3] B. D. Coleman and W. Noll, An approximation theorem for functionals with applications in continuum mechanics, Arch. Rational Mech. Anal. 6 (1960), 355-370.
• [4] G. V. Demidenko, The Cauchy problem for equations and systems of Sobolev type, in: Boundary Value Problems for Partial Differential Equations, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk 1986, 69-84 (in Russian).
• [5] G. V. Demidenko, The necessary conditions for the correct solvability of the Cauchy problem for the linearized system of Navier-Stokes equations, Sibirsk. Mat. Zh. 29 (3) (1988), 186-190 (in Russian).
• [6] G. V. Demidenko, The correct solvability of boundary value problems in a halfspace for quasielliptic equations, ibid. 29 (4) (1988), 54-67 (in Russian).
• [7] G. V. Demidenko, Boundary value problems for a class of pseudodifferential equations, in: Embedding Theorems and Their Applications to Problems in Mathematical Physics, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk 1989, 60-69 (in Russian).
• [8] G. V. Demidenko, The Cauchy problem for a certain hyperbolic system of the dynamics of stratified fluid, in: Boundary Value Problems for Partial Differential Equations, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk 1990, 56-76 (in Russian).
• [9] G. V. Demidenko, The Cauchy problem for generalized S. L. Sobolev equations, in: Functional Analysis and Mathematical Physics, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk 1985, 88-105 (in Russian).
• [10] G. V. Demidenko, Conditions for the solvability of mixed problems for a class of equations of Sobolev type, in: Boundary Value Problems for Partial Differential Equations, Trudy Sem. Sobolev. 1, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk 1984, 23-54 (in Russian).
• [11] G. V. Demidenko and I. I. Matveeva, On a certain class of boundary value problems for the Sobolev system, in: Partial Differential Equations, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk 1989, 54-78 (in Russian).
• [12] S. A. Gabov and A. G. Sveshnikov, Problems of the Dynamics of Stratified Fluids, Nauka, Moscow 1986 (in Russian).
• [13] S. A. Galpern, The Cauchy problem for general systems of linear partial differential equations, Trudy Moskov. Mat. Obshch. 9 (1960), 401-423 (in Russian).
• [14] H. P. Greenspan, On the transient motion of a contained rotating fluid, J. Fluid Mech. 20 (4) (1964), 673-696.
• [15] J. E. Lagnese, General boundary value problems for differential equations of Sobolev type, SIAM J. Math. Anal. 3 (1) (1972), 105-119.
• [16] J. Lighthill, Waves in Fluids, Cambridge Univ. Press, 1978.
• [17] V. N. Maslennikova, Solution of a mixed problem for non-stationary motion of a rotating viscous fluid and a study of the differential properties of the solution, Sibirsk. Mat. Zh. 2 (5) (1961), 708-718 (in Russian).
• [18] A. L. Pavlov, General boundary value problems for differential equations with constant coefficients in a half-space, Mat. Sb. 103 (3) (1977), 367-391 (in Russian).
• [19] C. G. Rossby, Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacement of the semi-permanent centers of action, J. Marine Res. 2 (1) (1939), 38-55.
• [20] R. E. Showalter, Partial differential equations of Sobolev-Galpern type, Pacific J. Math. 31 (3) (1969), 387-393.
• [21] R. E. Showalter and T. W. Ting, Pseudoparabolic partial differential equations, SIAM J. Math. Anal. 1 (1) (1970), 1-26.
• [22] S. L. Sobolev, Some new problems in mathematical physics, Izv. Akad. Nauk SSSR Ser. Mat. 18 (1954), 3-50 (in Russian).
• [23] S. V. Uspenskiĭ, The representation of functions defined by a certain class of hypoelliptic operators, Trudy Mat. Inst. Steklov. 117 (1972), 292-299 (in Russian).
• [24] S. V. Uspenskiĭ, G. V. Demidenko and V. G. Perepelkin, Embedding Theorems and Applications to Differential Equations, Nauka, Sibirsk. Otdel., Novosibirsk 1984 (in Russian).
Typ dokumentu
Bibliografia
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