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Comparison theorems for infinite systems of parabolic functional-differential equations

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Jaruszewska-Walczak D.

Annales Polonici Mathematici

2001

tom 77

nr 3

261-270

The paper deals with a weakly coupled system of functional-differential equations $∂_t u_i(t,x) = f_i(t,x,u(t,x),u,∂_x u_i(t,x),∂_{xx}u_i(t,x))$, i ∈ S, where (t,x) = (t,x₁,...,xₙ) ∈ (0,a) × G, $u = {u_i}_{i∈S}$ and S is an arbitrary set of indices. Initial boundary conditions are considered and the following questions are discussed: estimates of solutions, criteria of uniqueness, continuous dependence of solutions on given functions. The right hand sides of the equations satisfy nonlinear estimates of the Perron type with respect to the unknown functions. The results are based on a theorem on extremal solutions of an initial problem for infinite systems of ordinary functional-differential equations.

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On the Chaplygin method for the Darboux problem

100%

Jaruszewska-Walczak D.

Commentationes Mathematicae

2007

tom 47

nr 1

In the paper we deal with the Darboux problem for hyperbolic functional differential equations. We give the sufficient conditions for the existence of the sequence $\{z^{(m)}\}$ such that if $\tilde{z}$ is a classical solution of the original problem then $\{z^{(m)}\}$ is uniformly convergent to z$\tilde{z}$. The convergence that we get is of the Newton type.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Commentationes Mathematicae

2 Jaruszewska-Walczak D.

1 2007

1 2001

Wyniki wyszukiwania

Comparison theorems for infinite systems of parabolic functional-differential equations

On the Chaplygin method for the Darboux problem