Wave solutions travelling along quadratic paths for the equation $(\partial /\partial )-(k(u)u_{x})_{x}=0$
Author:
George H. Pimbley Jr.
Journal:
Quart. Appl. Math. 35 (1977), 129-138
MSC:
Primary 35B40; Secondary 35K05
DOI:
https://doi.org/10.1090/qam/440178
MathSciNet review:
440178
Full-text PDF Free Access
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D. B. Aronson, Regularity properties of flow through porous media, SIAM J. Appl. Math. 17, 461–467 (1969)
F. V. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rat. Mech. Anal. 42, 369–379 (1971)
H. Brezis, Monotonicity methods in Hilbert space and some applications to nonlinear partial differential equations, in Contributions to nonlinear functional analysis, E. Zarantonello ed., Academic Press, 1971
H. Brezis, Operateurs maximaux monotones el semigroupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies 5, North-Holland/American Elsevier, 1973
M. Crandall, Semigroups of nonlinear transformations in Banach spaces, in contributions to nonlinear functional analysis, E. Zarantonello ed., Adacemic Press, 1971
A. H. Craven and L. A. Peletier, Similarity solutions for degenerate quasilinear parabolic equations, J. Math. Anal. 38, 73–81 (1972)
J. Dorroh, A nonlinear Hille-Yosida-Phillips theorem, J. Funct. Anal. 3, 345–353 (1969)
T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19, 508–520 (1967)
L. Lions and E. Magenes, Problemes aux limites non homogenes el applications, Vol. 1, Dunod, 1968
G. Lumer and R. S. Phillips, Dissipative operators in Banach spaces, Pacific J. Math. 11, 679–698 (1961)
O. Oleinik, On some degenerate quasilinear parabolic equations, in Seminari dell ’Istituto Nazionalle di Alta Mathematica 1962–1963, Oderisi, Gublio, 355–371 (1964)
A. Pazy, Semi-groups of nonlinear contractions in Hilbert space, in Problems in nonlinear analysis, Prodi ed., CIME Varenna, Cremonese, 1971
L. A. Peletier, Asymptotic behavior of solutions of the, porous media equation, SIAM J. Appl. Math. 21, 542–551 (1971)
R. S. Phillips, Pertubation theory for semigroups of linear operators, Trans. A.M.S. 74, 199–221 (1953)
L. F. Shampine, Concentration-dependent diffusion II, Singular problems, Quart. Appl. Math. 31, 287–293 (1973)
E. C. Titchmarsh, Theory of functions, 2nd ed., Oxford, 1939
F. G. Tricomi, Integral equations, Interscience Publishers, N. Y., 1957
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© Copyright 1977
American Mathematical Society
