Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2020
Volume
Vol. 40
Number
No. 6
Description
Journal Volume
Opuscula Mathematica
Vol. 40 (2020)
Projects
Pages
Articles
General decay rate of a weakly dissipative viscoelastic equation with a general dampi
(Wydawnictwa AGH, 2020) Anaya, Khaleel; Messaoudi, Salim A.
In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.
Quasilinearization method for finite systems of nonlinear RL fractional differential equations
(Wydawnictwa AGH, 2020) Denton, Zachary; Ramírez, Juan Diego
In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order $0\lt q\lt 1$. Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.
A note on attractivity for the intersection of two discontinuity manifolds
(Wydawnictwa AGH, 2020) Difonzo, Fabio V.
In piecewise smooth dynamical systems, a co-dimension 2 discontinuity manifold can be attractive either through partial sliding or by spiraling. In this work we prove that both attractivity regimes can be analyzed by means of the moments solution, a spiraling bifurcation parameter and a novel attractivity parameter, which changes sign when attractivity switches from sliding to spiraling attractivity or vice-versa. We also study what happens at what we call attractivity transition points, showing that the spiraling bifurcation parameter is always zero at those points.
On the twisted Dorfman-Courant like brackets
(Wydawnictwa AGH, 2020) Mikulski, Włodzimierz M.
There are completely described all $\mathcal{VB}_{m,n}$-gauge-natural operators $C$ which, like to the Dorfman-Courant bracket, send closed linear $3$-forms $H\in\Gamma^{l-\rm{clos}}_E(\bigwedge^3T^*E)$ on a smooth $(\mathcal{C}^{\infty})$ vector bundle $E$ into $\mathbf{R}$-bilinear operators $C_H:\Gamma^l_E(TE\oplus T^*E)\times \Gamma^l_E(TE\oplus T^*E)\to \Gamma^l_E(TE\oplus T^*E)$ transforming pairs of linear sections of $TE\oplus T^*E\to E$ into linear sections of $TE\oplus T^*E\to E$. Then all such $C$ which also, like to the twisted Dorfman-Courant bracket, satisfy both some »restricted« condition and the Jacobi identity in Leibniz form are extracted.
Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains
(Wydawnictwa AGH, 2020) Nakao, Mitsuhiro
We consider the initial-boundary value problem for semilinear dissipative wave equations in noncylindrical domain $\bigcup_{0\leq t \lt\infty} \Omega(t)\times\{t\} \subset \mathbb{R}^N\times \mathbb{R}$. We are interested in finite energy solution. We derive an exponential decay of the energy in the case $\Omega(t)$ is bounded in $\mathbb{R}^N$ and the estimate $\int\limits_0^{\infty} E(t)dt \leq C(E(0),\|u(0)\|)\lt \infty$ in the case $\Omega(t)$ is unbounded. Existence and uniqueness of finite energy solution are also proved.