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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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