Existence, stability, and compactness in the $\alpha$-norm for partial functional differential equations
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- by C. C. Travis and G. F. Webb PDF
- Trans. Amer. Math. Soc. 240 (1978), 129-143 Request permission
Abstract:
The abstract ordinary functional differential equation $(a/dt)u(t) = - Au(t) + F({u_t}),{u_0} = \phi$, is studied, where $- A$ is the infinitesimal generator of an analytic semigroup of linear operators and F is continuous with respect to a fractional power of A.References
- C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395–418. MR 382808, DOI 10.1090/S0002-9947-1974-0382808-3
- C. C. Travis and G. F. Webb, Partial differential equations with deviating arguments in the time variable, J. Math. Anal. Appl. 56 (1976), no. 2, 397–409. MR 415102, DOI 10.1016/0022-247X(76)90052-4 D. Henry, Geometric theory of nonlinear parabolic equations (to appear).
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 240 (1978), 129-143
- MSC: Primary 34G05; Secondary 35R10
- DOI: https://doi.org/10.1090/S0002-9947-1978-0499583-8
- MathSciNet review: 0499583