The Existence and Uniqueness of Solutions of a Class of Evolution Equations

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Volume 8, Issue 3

Lushan Yang & Deming Shi

J. Part. Diff. Eq., 8 (1995), pp. 233-241.

Published online: 1995-08

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Abstract

In this paper, a class of evolution equations which have special boundary conditions is discussed. The spectrum properties of an operator which is associated with this class of equations arc provided, and the existence and uniqueness of solutions of this class of equations is proved by the theory of pertu rbation of C_0-semigroups. In the last part of this paper, a condition which ensures the solutions to be non-negative is given. Some results of the time-independent population systems in [1-5] are our examples.

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Evolution equation C_0-semigroup

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@Article{JPDE-8-233, author = {Yang , Lushan and Shi , Deming}, title = {The Existence and Uniqueness of Solutions of a Class of Evolution Equations}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {3}, pages = {233--241}, abstract = { In this paper, a class of evolution equations which have special boundary conditions is discussed. The spectrum properties of an operator which is associated with this class of equations arc provided, and the existence and uniqueness of solutions of this class of equations is proved by the theory of pertu rbation of C_0-semigroups. In the last part of this paper, a condition which ensures the solutions to be non-negative is given. Some results of the time-independent population systems in [1-5] are our examples.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5655.html} }

TY - JOUR T1 - The Existence and Uniqueness of Solutions of a Class of Evolution Equations AU - Yang , Lushan AU - Shi , Deming JO - Journal of Partial Differential Equations VL - 3 SP - 233 EP - 241 PY - 1995 DA - 1995/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5655.html KW - Evolution equation KW - C_0-semigroup AB - In this paper, a class of evolution equations which have special boundary conditions is discussed. The spectrum properties of an operator which is associated with this class of equations arc provided, and the existence and uniqueness of solutions of this class of equations is proved by the theory of pertu rbation of C_0-semigroups. In the last part of this paper, a condition which ensures the solutions to be non-negative is given. Some results of the time-independent population systems in [1-5] are our examples.

Yang , Lushan and Shi , Deming. (1995). The Existence and Uniqueness of Solutions of a Class of Evolution Equations. Journal of Partial Differential Equations. 8 (3). 233-241. doi:

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