General finite difference approximation to the Cauchy problem for nonlinear parabolic differential-functional equations
Generalized Cauchy problems for hyperbolic functional differential systems
A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.
Generalized method of lines for first order partial functional differential equations
Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization...
Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form
Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations
Generalized solutions to quasilinear hyperbolic systems in the second canonical form are investigated. A theorem on existence, uniqueness and continuous dependence upon the boundary data is given. The proof is based on the methods due to L. Cesari and P. Bassanini for systems which are not functional.
Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models
In this paper, we discuss the special diffusive hematopoiesis model with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.
Global Attractor for a Class of Parabolic Equations with Infinite Delay
We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.
Global existence for functional semilinear integro-differential equations
In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps.
Global existence, uniqueness, and continuous dependence for a reaction-diffusion equation with memory.
Global solvability of the mixed problem for first order functional partial differential equations
Global uniqueness results for fractional order partial hyperbolic functional differential equations.
Global uniqueness results for fractional partial hyperbolic differential equations with state-dependent delay
We investigate the existence and uniqueness of solutions of hyperbolic fractional order differential equations with state-dependent delay by using a nonlinear alternative of Leray-Schauder type due to Frigon and Granas for contraction maps on Fréchet spaces.