Remarks concerning the supports of solutions of pseudoparabolic equations
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- by William Rundell and Michael Stecher PDF
- Proc. Amer. Math. Soc. 63 (1977), 77-81 Request permission
Abstract:
This paper deals with the existence of nontrivial solutions of the pseudoparabolic equation ${u_{xxt}} - {u_t} + {u_{xx}} = 0$ whose supports lie in the half spaces $t > {t_0},x > {x_0}$. In addition, we show the nonexistence of solutions whose supports lie in bounded strips in x or t.References
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G. Barenblat, I. Zheltov and I. Kochiva, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech. 24 (1960), 1286-1303.
P. J. Chen and M. E. Gurtin, On a theory of heat conduction involving two temperatures, Z. Angew. Math. Phys. 19 (1968), 614-627.
- David Colton, Pseudoparabolic equations in one space variable, J. Differential Equations 12 (1972), 559–565. MR 326131, DOI 10.1016/0022-0396(72)90025-3 G. Hellwig, Partial differential equations, Blaisdell, Waltham, Mass., 1964.
- Lars Hörmander, Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften, Band 116, Springer-Verlag New York, Inc., New York, 1969. Third revised printing. MR 0248435 E. H. Milne, The diffusion of imprisoned radiation through a gas, J. London Math. Soc. 1 (1926), 40-51.
- William Rundell and Michael Stecher, A method of ascent for parabolic and pseudoparabolic partial differential equations, SIAM J. Math. Anal. 7 (1976), no. 6, 898–912. MR 420015, DOI 10.1137/0507071
- R. E. Showalter and T. W. Ting, Pseudoparabolic partial differential equations, SIAM J. Math. Anal. 1 (1970), 1–26. MR 437936, DOI 10.1137/0501001
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 77-81
- MSC: Primary 35K25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0433037-4
- MathSciNet review: 0433037