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36 papers · 1 filter
Large free linear algebras of real and complex functions
Artur Bartoszewicz, Szymon Gł\cab, Adam Paszkiewicz
Let be a set of cardinality such that . We prove that the linear algebra (or ) contains a free linear algebra with generators. Usi…
Exact solutions of nonlinear boundary value problems of the Stefan type
Roman Cherniha, Sergii Kovalenko
The (1+1)-dimensional nonlinear boundary value problem, modeling the process of melting and evaporation of metals, is studied by means of the classical Lie symmetry method. All pos…
Lie symmetry of a class of nonlinear boundary value problems with free boundaries
Roman Cherniha, Sergii Kovalenko
A class of (1+1)--dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie…
Lie symmetries and reductions of multi-dimensional boundary value problems of the Stefan type
Roman Cherniha, Sergii Kovalenko
A new definition of Lie invariance for nonlinear multi-dimensional boundary value problems (BVPs) is proposed by the generalization of known definitions to much wider classes of BV…
Attractivity and stability in the competitive systems of PDEs of Kolmogorov type
Joanna Balbus
We consider -species nonautonomous competitive systems of partial differential equations of Kolmogorov type. Under the Neumann boundary conditions we give a sufficient condition…
Pointwise products of some Banach function spaces and factorization
Paweł Kolwicz, Karol Leśnik, Lech Maligranda
The well-known factorization theorem of Lozanovski{\u ı} may be written in the form , where means the pointwise product of Banach ideal spac…