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Singularly perturbed pseudoparabolic equation. (English) Zbl 1366.35100

Summary: An asymptotic expansion of the contrasting structure-like solution of the generalized Kolmogorov-Petrovskii-Piskunov equation is presented. A generalized maximum principle for the pseudoparabolic equations is developed. This, together with the generalized differential inequalities method, allows to prove the consistence and convergence of the asymptotic series method.

MSC:

35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
34E05 Asymptotic expansions of solutions to ordinary differential equations
35C20 Asymptotic expansions of solutions to PDEs
35B50 Maximum principles in context of PDEs
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