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1
Content available Global solutions for a nonlinear Kirchhoff type equation with viscosity
Lapa Eugenio Cabanillas
Opuscula Mathematica
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2023
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Vol. 43, no. 5
689--701
EN
In this paper we consider the existence and asymptotic behavior of solutions of the following nonlinear Kirchhoff type problem [formula] where [formula]. If the initial energy is appropriately small, we derive the global existence theorem and its exponential decay.
2
Content available remote Minimizing movements for dissipative systems that are not gradient flows
Mimura Yoshifumi
Bulletin of the Polish Academy of Sciences. Mathematics
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2022
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Vol. 70, no. 2
133--149
EN
The time discretization method, which is a method of constructing time global solutions for gradient flows, is applied to dissipative systems in Hilbert spaces, which are not necessarily gradient flows. Equations with perturbation terms added to gradient flows are considered, and when the perturbation term is smaller than the principal term in an analytical sense, the dissipative structure of the energy is maintained, and the existence of time global solutions is shown by the time discretization method.
3
Content available remote On the Existence of a Non-trivial Non-negative Global Radial Weak Solution to a Fractional Laplacian Problem with a Singular Potential
Bayrami M., Hesaaraki M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2016
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Vol. 64, no. 2/3
175--183
EN
We prove the existence of a non-trivial non-negative radial weak solution to the problem [wzór]. Here N > 2α, α ∈ (1/2,1), 1 < r < p < [wzór] and μ ∈ R. We also assume that b > 0 and 0 < λ < [wzór].
4
Content available Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity
Nakao M.
Opuscula Mathematica
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2014
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Vol. 34, no. 3
569--590
EN
We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a ‘loan’ method and use a difference inequality on the energy.
5
Content available remote Impulsive functional-differential equations of first order
Skóra L.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
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Vol. 47, [Z] 2
207-219
EN
In this paper we present some existence results for impulsive functionaldifferential equations of first order.
6
Content available remote Global solution to the initial value problem for nonlinear system of equations of thermodiffusion without displacements
Łazuka J.
Demonstratio Mathematica
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2004
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Vol. 37, nr 3
557--570
EN
In the paper we shall present the proof of global-in-time solution to the initial value problem for nonlinear partial differential equations describing physical proc-cesses of thermodiffusion without displacements. Time decay of global solution will be also shown.
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