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Asymptotic behavior and traveling wave solutions for parabolic functional differential equations. (English) Zbl 0637.35082
L’A. étudie l’équation parabolique différence-différentielle $$ \partial\sb tu- \partial\sp 2\sb xu= f(u(x,t),u(x,t-c)),\quad \tau \in R\sp+, $$ avec $f(0,0)=f(1,1)=0$, $\partial\sp 2f(r,s)\ge 0$, $0\le r,s\le 1$, et démontre plusieurs théorèmes, pour lesquels on renvoit au mémoire. L’A. étudie la propagation des ondes et démontre l’existence d’une vitesse minimum et asymptotique. On emploit la théorie des équations fonctionnelles différentielles et le principe de maximum pour équations fonctionnelles différentielles paraboliques. On étudie le cas, dans lequel f admet un équilibre OL comprisenter 0 et 1; on étudie aussi la stabilité de la propagation des ondes.

35R10Partial functional-differential equations
35K55Nonlinear parabolic equations
35B40Asymptotic behavior of solutions of PDE
35B35Stability of solutions of PDE
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35K10Second order parabolic equations, general
34K10Boundary value problems for functional-differential equations
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