Summary
In this paper we consider the pseudo-parabolic equations arising in the filtration of water in media with double porosity and moisture transfer in soil. The existence, uniqueness and stability for both classical and weak solutions are studied.
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B. D. Coleman -R. J. Duffin -V. J. Mizel,Instability, uniqueness, and nonexistence theorem for the equation u t=u xx−u xtx on a strip, Arch. Rat. Mech. Anal.,19 (1965), pp. 100–116.
B. D. Coleman -W. Noll,An approximation theorem for functionals, with application in continuum mechanics, Arch. Rat. Mech. Anal.,6 (1960), pp. 355–370.
D. Colton,Pseudoparabolic equation in one space variable, J. Diff. Eq.,12 (1972), pp. 559–565.
A. F. Chudnovski,Soil Thermophysics, Nauka, Moscow (1976).
William -Rundell,The construction of solutions to pseudo parabolic equation in non-cylindrical domains, J. Diff. Eq.,27 (1978), pp. 394–404.
G. I. Barenblat -Yu. P. Zhelton -I. V. Kochina,Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks[strata], PMM J. Appl. Math. Mech.,24, No. 5 (1960), pp. 852–864.
M. Kh. Shkhanukov,Boundary-value problem for a third-order equation occurring in the modeling of water filtration in porous midia, Diff. Eqs.,18, No. 4 (1982), pp. 189–699.
R. E. Showalter,Partial differential equations of Sobolev-Galpern type, Pacific J. Math.,31 (1969), pp. 787–794.
R. E. Showalter,The Sobolev equation I, Applicable Analysis,5 (1975), pp. 15–22.
R. E. Showalter,The Sobolev equation II, Applicable Analysis,5 (1975), pp. 81–99.
R. E. Showalter,Sobolev equations for nonlinear dispersive system, Applicable Analysis,7 (1978), pp. 293–308.
R. E. Showalter,Local regularity, boundary values and maximum principle for pseudo-parabolic equations, Applicable Analysis,16 (1983), pp. 235–241.
R. E. Showalter -T. W. Ting,Pseudo-parabolic partial differential equations, SIAM J. Math. Anal.,1 (1970), pp. 1–26.
T. W. Ting,Certain non-steady flows of second order fluids, Arch. Rat. Mech. Anal.,14 (1963), pp. 1–26.
V. A. Vodakhova,A boundary value problem with A. M. Nakhushev's nonlocal condition for a pseudoparabolic moisture-transfer equation, Diff. Eqs.,18, No. 2 (1982), pp. 280–285.
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Cannon, J.R., Lin, Y. Classical and weak solutions for one-dimensional pseudo-parabolic equations with typical boundary data. Annali di Matematica pura ed applicata 152, 375–385 (1988). https://doi.org/10.1007/BF01766158
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DOI: https://doi.org/10.1007/BF01766158