We prove the existence of inertial manifolds for partial functional differential equation du(t)dt+Au(t)=F(t)ut+g(t,ut) under the conditions that the partial differential operator 𝐴 is positive such ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear ...