Browsing by Subject "Cauchy problem"

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Access status: Restricted ,
Metoda prostych dla nieliniowych równań różniczkowo-funkcyjnych na piramidzie Haara
(Data obrony: 2009-06-30) Nabożny, Anna
Wydział Matematyki Stosowanej
Access status: Open Access ,
Monotone iteration for infinite systems of parabolic equations
(2005) Pudełko, Anna
In the paper the Cauchy problem for an inﬁnite system of parabolic type equations is studied. The general operators of the parabolic type of second order with variable coefficients are considered and the system is weakly coupled. Among the obtained results there is a theorem on diffenential inequality as well as the existence and uniqueness theorem in the class of continuous-bounded functions obtained by monotone iterative method.
Access status: Open Access ,
On k-summability of formal solutions for certain partial differential operators with polynomial coefficients
(2015) Ichinobe, Kunio; Miyake, Masatake
We study the $k$-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in $t$. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.
Access status: Open Access ,
Parametric formal Gevrey asymptotic expansions in two complex time variable problems
(Wydawnictwa AGH, 2026) Chen, Guoting; Lastra, Alberto; Malek, Stéphane
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an auxiliary problem in the Borel plane overcomes the absence of adequate domains which would guarantee summability of the formal solution. Moreover, several exponential decay rates of the difference of analytic solutions with respect to the perturbation parameter at the origin are observed, leading to several asymptotic levels relating the analytic and the formal solution
Access status: Open Access ,
Some analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations. Part 1
(2006) Pytel-Kudela, Marzena; Prykarpatski, Anatolij
The analytical properties of dissolving operators related with the Cauchy problem for a class of nonautonomous partial differential equations in Hilbert spaces are studied using theory of bilinear forms in respectively rigged Hilbert spaces triples. Theorems specifying the existence of a dissolving operator for a class of adiabatically perturbed nonautonomous partial differential equations are stated. Some applications of the results obtained are discussed.
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Zbieżność rozwiązań nieliniowego, nielokalnego zagadnienia Cauchy'ego do fali rozrzedzeniowej
(Data obrony: 2014-09-15) Krówczyński, Michał
Wydział Matematyki Stosowanej