Geodesic
Boundary-Value Problems of a Degenerate Sobolev-Type Differential Equation
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 221-228

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this paper is to study a degenerate Sobolev type partial differential equation in the form of Mut + Lu = f, where M and L are second order partial differential operators defined in a domain (0, T]×Ω in R n+1. The degenerate property of the equation is in the sense that both M and L are not necessarily strongly elliptic and their coefficients may vanish or be negative in some part of the domain (0, T]×Ω. Two types of boundary conditions are investigated. 
Pao, C. V. Boundary-Value Problems of a Degenerate Sobolev-Type Differential Equation. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 221-228. doi: 10.4153/CMB-1977-035-5
@article{10_4153_CMB_1977_035_5,
     author = {Pao, C. V.},
     title = {Boundary-Value {Problems} of a {Degenerate} {Sobolev-Type} {Differential} {Equation}},
     journal = {Canadian mathematical bulletin},
     pages = {221--228},
     year = {1977},
     volume = {20},
     number = {2},
     doi = {10.4153/CMB-1977-035-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-035-5/}
}
TY  - JOUR
AU  - Pao, C. V.
TI  - Boundary-Value Problems of a Degenerate Sobolev-Type Differential Equation
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 221
EP  - 228
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-035-5/
DO  - 10.4153/CMB-1977-035-5
ID  - 10_4153_CMB_1977_035_5
ER  - 
%0 Journal Article
%A Pao, C. V.
%T Boundary-Value Problems of a Degenerate Sobolev-Type Differential Equation
%J Canadian mathematical bulletin
%D 1977
%P 221-228
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-035-5/
%R 10.4153/CMB-1977-035-5
%F 10_4153_CMB_1977_035_5

[1] 1. Barenblat, G., Zheltor, I., and Kochiva, I., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech., 24 (1960), 1286-1303. Google Scholar

[2] 2. Chen, P. and Gurtin, M., On a theory of heat conduction involving two temperatures, Z. Angew. Math. Phys., 19 (1968), 614-627. Google Scholar

[3] 3. Ford, W. T., The first initial boundary-value problem for a non-uniform parabolic equation, J. Math. Anal. Appl., 40 (1972), 131-137. Google Scholar

[4] 4. Ivanov, A. V.,A boundary value problem for degenerate second order parabolic linear equations (Russian), Zap. Nauch. Sem. Leningrad Otdel. Math. Inst. Steklov., 14 (1969), 48-88. Google Scholar

[5] 5. Lagnese, J., General boundary value problems for differential equations of Sobolev-Galpern type, SIAM J. Math. Anal., 3 (1972), 105-119. Google Scholar

[6] 6. Lions, J. L., Equations Différentielles Operationelles, Springer-Verlag, Berlin, 1961. Google Scholar

[7] 7. Oleinnik, O. A., On the smoothness of the solutions of degenerate elliptic and parabolic equations, Soviet Math. Dokl., 6 (1965), 972-976. Google Scholar

[8] 8. Pao, C. V., On a non-uniform parabolic equation with mixed boundary condition, Proc. Amer. Math. Soc., 49 (1975), 83-89. Google Scholar

[9] 9. Rao, V. R. Gopala and Ting, T. W., Solutions of pseudo-heat equations in whole space, Arch. Rational Mech. Anal., 49 (1972), 57-78. Google Scholar

[10] 10. Showalter, R. E., Degenerate evolution equations and applications, Indiana Univ. Math. J., 23 (1974), 655-677. Google Scholar

[11] 11. Sobolev, V. V., A Treatise on Radiative Transfer, Van Nostrand, New York, 1963. Google Scholar

[12] 12. Ting, T. W., Certain non-study flows of second order fluids, Arch. Rational Mech. Anal., 14 (1963), 1-26. Google Scholar

Cité par Sources :