Kazantsev, Yu. I. A new method for solving nonlinear nonstationary equations (case of one space variable). (English. Russian original) Zbl 0493.35052 Math. Notes 31, 110-114 (1982); translation from Mat. Zametki 31, 215-221 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 35K55 Nonlinear parabolic equations 35D05 Existence of generalized solutions of PDE (MSC2000) 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) 46F99 Distributions, generalized functions, distribution spaces Keywords:generalized Hardy functions; nonlinear transient equation; polynomial type nonlinearity; uniqueness; existence; system of nonlinear convolution type integral equations PDFBibTeX XMLCite \textit{Yu. I. Kazantsev}, Math. Notes 31, 110--114 (1982; Zbl 0493.35052); translation from Mat. Zametki 31, 215--221 (1982) Full Text: DOI References: [1] J. L. Lions, Non-Homogeneous Boundary-Value Problems and Applications, Springer-Verlag (1972). [2] V. K. Kalantarov and O. A. Ladyzhenskaya, ?Collapsing solutions of quasilinear equations of parabolic and hyperbolic types,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,6, No. 10, 77-102 (1977). · Zbl 0354.35054 [3] A. V. Babin, ?Global solvability of nonlinear parabolic boundary-value problems,? Mat. Sb.,97, No. 1, 94-109 (1975). · Zbl 0323.35048 [4] H. J. Bremermann, Distributions, Complex Variables, and Fourier Transforms, Addison-Wesley (1965). · Zbl 0151.18102 [5] L. S. Sobolev, ?Some new problems in the theory of hyperbolic partial differential equations,? Mat. Sb.,11, No. 3, 155-203 (1942). · Zbl 0061.21509 [6] A. N. Tikhonov and A. A. Samarskii, The Equations of Mathematical Physics [in Russian], Nauka, Moscow (1953). · Zbl 0044.09302 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.