Displaying similar documents to “Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type”

Comparison of explicit and implicit difference methods for quasilinear functional differential equations

W. Czernous, Z. Kamont (2011)

Applicationes Mathematicae

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We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties...

Sufficient conditions for the solvability of some third order functional boundary value problems on the half-line

Hugo Carrasco, Feliz Minhós (2017)

Commentationes Mathematicae Universitatis Carolinae

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This paper is concerned with the existence of bounded or unbounded solutions to third-order boundary value problem on the half-line with functional boundary conditions. The arguments are based on the Green functions, a Nagumo condition, Schauder fixed point theorem and lower and upper solutions method. An application to a Falkner-Skan equation with functional boundary conditions is given to illustrate our results.

The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below

Tomasz Cieślak (2006)

Banach Center Publications

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In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.

Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations

Stanisław Brzychczy (2001)

Annales Polonici Mathematici

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We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.