Theorems about the Existence of Solutions to Problems with Nonlocal Initial Value

Acta Mathematica Sinica, English Series

Volumn 17, Issue 2, 2001, Pages 197-206

  Wang, Yuan Di ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Existence; Generalized Poincare e operator; Nonlinear boundary condition; Nonlocal problem; Parabolic equation; Solution

Indexed keywords

EID: 0346977368     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101140100115     Document Type: Article

References (13)

1. A. Kerefov, Non-local boundary value problems for parabolic equations, Differentsial'nya Uravaneiya, 1979, 15: 74-78.
2. P. Vabishchevich, Nonlocal parabolic problems and the inverse heat-conduction problem, Differentsial'nya Uravneniya, 1981, 17: 1193-1199.
3. J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math J, 1984, 93: 109-131.
4. L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J Math. Anal. Appl., 1991, 162: 494-505.
5. K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl., 1993, 179: 630-637.
6. C. Pao, Reaction-diffusion equations with nonlocal bounday and nonlocal initial conditions, J. Math. Anal. Appl., 1995, 195: 702-718.
7. Y. Lin, J. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal TMA, 1996, 26(5): 1023-1033.
8. H. Amann, Periodic solutions of semilinear parabolic equations, Nonlinear Analysis, A Collection of Papers in Honor of Erich H Rothe, edited by L Cesari, R Kanna and H F Weinberger, New York/San Francisco/London: Academic Press, 1978, 1-29.
9. X. Xiang, T. Luo, Existence of periodic solutions of nonlinear systems with nonlinear boundary conditions, Acta Math. Sinica, New Series, 1995, 11(4): 439-445.
10. H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Diff. Eqs., 1988, 72: 201-269.
11. P. Grisvard, Équations différentielles abstraites, Ann. Sci Éc Norm Sup, Sér 1969, 4: 311-395.
12. p with boundary conditions, Stud Math., 1972, 44: 47-60.
13. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, New York, Berlin: Heideberg, Tokyo: Springer-Verlag, 1983.