On the global solution of some nonlinear parabolic equation

MR0605330 Ebihara, Yukiyoshi and Nanbu, Tokumori Yukiyoshi EBIHARA and Tokumori NANBU On the global solution of some nonlinear parabolic equation Funkcialaj Ekvacioj. Serio Internacia 20 1977 23--38 http://fe.math.kobe-u.ac.jp/FE/Free/vol20/fe20-1-3.pdf http://fe.math.kobe-u.ac.jp/FE/FE_pdf_with_bookmark/FE11-20-en_KML/fe20-023-038/fe20-023-038.pdf http://www.ams.org/mathscinet-getitem?mr=MR0605330 fe20-023-038 1977 On the Global Solution of Some Nonlinear Parabolic Equation EBIHARA, Yukiyoshi; NANBU, Tokumori EBIHARA, Yukiyoshi; NANBU, Tokumori 1 Adams, R. A. Sobolev Spaces Academic Press, New York 1975 MR0450957 100 Cache/Ad/Adams,Sobolev,*,1975,1976 xviii+268 2 Coddington, E. A.; Levinson, N. Theory of Ordinary Differential Equations Mc- Graw-Hill, New York 1955 MR0069338 100 Cache/Co/Coddington,Ordinary,*,1955,1956 xii+429

3 Dionne, P. A. Sur les problemes de Cauchy hyperboliques bien posés J. Analyse Math. 10 1962/1963 1-90 MR0150475 100 Cache/Di/Dionne,hyperboliques,J*,1962,1963

4 Ebihara, Y. On the local classical solution of the mixed problem for nonlinear wave equation Math. Rep. College General Ed., Kyushu Univ. IX 1973/1974 43-65 MR0569678 100 Cache/Eb/Ebihara,classical,Math*,1974,1975

5 Ebihara, Y. On the global classical solutions of nonlinear wave equations Funkcial Ekvac. 18 3 1975 227-244 MR0415086 0415086 100 Cache/Eb/Ebihara,classical,Funkcial*,1975,1976 6 Ebihara, Y., On the Classical Solution of the Initial Value Problem for a Nonlinear Wave Equation, (to appear) MR0546985 7 Friedman, A. Partial Differential Equations of Parabolic Type Prentice-Hall 1964 MR0181836 Cache/Fr/Friedmann,Partial,*,1964,1965

8 Fujita, H. On the blowing up of solutions of the Cauchy Problem for $u_t=\Delta u+u^{1+a}$ J. Fac. Sci. Univ. Tokyo Sect I I 13 1966 109-124 MR0214914 84 Cache/Fu/Fujita,solutions,J*,1966,1967

9 Kaplan, S. On the growth of solutions of quasi-linear parabolic equations Comm. Pure. Appl. Math. 16 1963 305-330 MR0160044 100 Cache/Ka/Kaplan,quasi-linear,Comm*,1963,1964

10 Ladyzenskaja, O. A.; Solonnikov, V. A.; Uralceva, N. N. Linear and Quasi-linear Equations of Parabolic Type A. M. S. 1968 MR0241822 85 Cache/La/Ladyzenskaja,Quasi-linear,*,1968,1969 xi+648 11 Mizohata, S. The theory of partial differential equations Iwanami, Tokyo 1965 (in Japanese) viii+462 MR0232070

12 Oleinik, O. A.; Kruzhkov, S. N. Quasi-linear second-order parabolic equations with many independent variables Uspehi. Mat. Nauk 16 1961 115-155 MR0141892 87 Cache/Ol/Oleinik,Quasi-linear,Uspehi*,1961,1962

13 Pao, C. V. Successive Approximations of Some Nonlinear Initial-Boundary Value Problems SIAM. J. Math. Anal. 5 1 1974 91-102 MR0339507 100 Cache/Pa/Pao,Initial-Boundary,SIAM*,1974,1975

14 Pontrjagin, L. S. Ordinary Differential Equations Kyoritsu Tokyo 1963 (translation in Japanese) 000 MR0140742 Cache/Po/Pontrjagin,Ordinary,*,1963,1964 15 Sobolev, S. L. Some applications of functional analysis to mathematical physics Leningrad 1950 MR0052039 16 Tsutsumi, M. Existence and Nonexistence of Global Solutions of the First Boundary Value Problem for a Certain Quasilinear Parabolic Equations Funkcial. Ekvac. 17 1974 13-24 MR0344679 0344679 Cache/Ts/Tsutsumi,Non-existence,Funkcial*,1974,1975