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Well-posed problem of nonlinear singular distributed parameter systems and nonlinear GE-semigroup

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Abstract

According to the well-posed problem of nonlinear singular distributed parameter systems, first of all, the nonlinear GE-semigroup induced by a continuous (possibly nonlinear) operator is introduced in Banach space, which is a generalization of GE-semigroup (i.e., generalized operator semigroup), and the properties of nonlinear GE-semigroup are discussed; and then the existence, uniqueness and constructive expression for the strong solution of nonlinear singular distributed parameter system are discussed by nonlinear GE-semigroup; at last, the exponential stability of nonlinear singular distributed parameter system is studied by using nonlinear GE-semigroup, functional analysis and operator theory in Banach space.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China

    ZhaoQiang Ge

  2. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing, 100190, China

    DeXing Feng

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  1. ZhaoQiang Ge
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  2. DeXing Feng
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Correspondence to ZhaoQiang Ge.

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Ge, Z., Feng, D. Well-posed problem of nonlinear singular distributed parameter systems and nonlinear GE-semigroup. Sci. China Inf. Sci. 56, 1–14 (2013). https://doi.org/10.1007/s11432-013-4852-3

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  • DOI: https://doi.org/10.1007/s11432-013-4852-3

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