# Comparison theorems for infinite systems of parabolic functional-differential equations

Annales Polonici Mathematici (2001)

- Volume: 77, Issue: 3, page 261-270
- ISSN: 0066-2216

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topDanuta Jaruszewska-Walczak. "Comparison theorems for infinite systems of parabolic functional-differential equations." Annales Polonici Mathematici 77.3 (2001): 261-270. <http://eudml.org/doc/280502>.

@article{DanutaJaruszewska2001,

abstract = {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.},

author = {Danuta Jaruszewska-Walczak},

journal = {Annales Polonici Mathematici},

keywords = {nonlinear estimates of the Perron type; estimates of solutions; uniqueness; continuous dependence},

language = {eng},

number = {3},

pages = {261-270},

title = {Comparison theorems for infinite systems of parabolic functional-differential equations},

url = {http://eudml.org/doc/280502},

volume = {77},

year = {2001},

}

TY - JOUR

AU - Danuta Jaruszewska-Walczak

TI - Comparison theorems for infinite systems of parabolic functional-differential equations

JO - Annales Polonici Mathematici

PY - 2001

VL - 77

IS - 3

SP - 261

EP - 270

AB - 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.

LA - eng

KW - nonlinear estimates of the Perron type; estimates of solutions; uniqueness; continuous dependence

UR - http://eudml.org/doc/280502

ER -

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