Physics

Nonlinear system

Operator (biology)

Mathematics

Transcription factor

Biology

Partial differential equation

Gene

Regular polygon

Mathematical analysis

Cauchy problem

Artificial intelligence

Repressor

Initial value problem

Chemistry

Parabolic partial differential equation

Ecology

Class (philosophy)

Geometry

Type (biology)

Measure (data warehouse)

Evolution equation

Computer science

Cauchy distribution

Quantum mechanics

Applied mathematics

Fixed-point theorem

Biochemistry

Database

Discrete and Continuous Dynamical Systems - B

This paper investigates the Cauchy problem to a class of stochastic non-autonomous evolution equations of parabolic type governed by noncompact evolution families in Hilbert spaces. Combining the theory of evolution families, the fixed point theorem with respect to convex-power condensing operator and a new estimation technique of the measure of noncompactness, we established some new existence results of mild solutions under the situation that the nonlinear function satisfy some appropriate local growth condition and a noncompactness measure condition. Our results generalize and improve some previous results on this topic, since the strong restriction on the constants in the condition of noncompactness measure is completely deleted, and also the condition of uniformly continuity of the nonlinearity is not required. At last, as samples of applications, we consider the Cauchy problem to a class of stochastic non-autonomous partial differential equation of parabolic type.

Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families