Manuscript Topics

Evolutionary partial differential equations, i.e., partial differential equations with time t as one of the independent variables, arise not only from many fields of mathematics, but also from other branches of science such as physics, mechanics and material science. For example, wave and plate equations, Navier-Stokes and Euler equations, reaction-diffusion equations, Timoshenko type equations, etc, are special examples of evolutionary partial differential equation. The theoretical study of these equations have attracted a lot of interest from many mathematicians and scientists in linear and nonlinear sciences. A series of useful methods and theories have been developed, such as the semigroup method, multiplier method, compactness and monotone operator method, and so on. Many results of existence, uniqueness and asymptotic behavior can then be established from the corresponding results for some evolutionary partial differential equations. The aim of this special issue is to collect original and high-quality contributions related to the development of the theory of some evolution equations. Topics to be included: existence and uniqueness results, asymptotic behavior, control theory and long-time dynamics for linear/nonlinear evolution equations arising in sciences and engineering.

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