The Solvability for a Class of Nonlinear Integrodifferential Equations of Parabolic Type

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Volume 5, Issue 3

Yin Hongming

J. Part. Diff. Eq.,5(1992),pp.46-60

Published online: 1992-05

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Abstract

In this paper we consider the well-posedness for a class of nonlinear integrodifferential equations of parabolic type. We use integral estimates to deduce an a priori estimate in the classical space C^{2+α,1+\frac{α}{2}}. The existence of the solution is established by means of the continuity method which is similar to a parabolic initial and boundary value problem. Moreover, the continuous dependence upon the data and the uniqueness of the solution are obtained. Finally, the results are generalized into a class of nonlinear integrodifferential systems.

Keywords

Integrodifferential equation nonlinearity global solvability

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@Article{JPDE-5-46, author = {Yin Hongming}, title = {The Solvability for a Class of Nonlinear Integrodifferential Equations of Parabolic Type}, journal = {Journal of Partial Differential Equations}, year = {1992}, volume = {5}, number = {3}, pages = {46--60}, abstract = { In this paper we consider the well-posedness for a class of nonlinear integrodifferential equations of parabolic type. We use integral estimates to deduce an a priori estimate in the classical space C^{2+α,1+\frac{α}{2}}. The existence of the solution is established by means of the continuity method which is similar to a parabolic initial and boundary value problem. Moreover, the continuous dependence upon the data and the uniqueness of the solution are obtained. Finally, the results are generalized into a class of nonlinear integrodifferential systems.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5744.html} }

TY - JOUR T1 - The Solvability for a Class of Nonlinear Integrodifferential Equations of Parabolic Type AU - Yin Hongming JO - Journal of Partial Differential Equations VL - 3 SP - 46 EP - 60 PY - 1992 DA - 1992/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5744.html KW - Integrodifferential equation KW - nonlinearity KW - global solvability AB - In this paper we consider the well-posedness for a class of nonlinear integrodifferential equations of parabolic type. We use integral estimates to deduce an a priori estimate in the classical space C^{2+α,1+\frac{α}{2}}. The existence of the solution is established by means of the continuity method which is similar to a parabolic initial and boundary value problem. Moreover, the continuous dependence upon the data and the uniqueness of the solution are obtained. Finally, the results are generalized into a class of nonlinear integrodifferential systems.

Yin Hongming. (1992). The Solvability for a Class of Nonlinear Integrodifferential Equations of Parabolic Type. Journal of Partial Differential Equations. 5 (3). 46-60. doi:

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