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9 p, 290.7 KB |
Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
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Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Vulpe, Nicolae (Vladimir Andrunakievichi Institute of Mathematics and Computer Science (Moldova))
The following differential quadratic polynomial differential system dx/dt=y−x, dy/dt=2y−y/y−1(2−yy−5y−4/y−1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. [...]
2024 -  10.3390/appliedmath4010004
AppliedMath, Vol. 4, Issue 1 (January 2024) , p. 70-78
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13 p, 959.5 KB |
Symmetric Phase Portraits of Homogeneous Polynomial Hamiltonian Systems of Degree 1, 2, 3, 4, and 5 with Finitely Many Equilibria
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Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi. Department of Mathematics) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Roughly speaking, the Poincaré disc D2 is the closed disc centered at the origin of the coordinates of R2, where the whole of R2 is identified with the interior of D2 and the circle of the boundary of D2 is identified with the infinity of R2, because in the plane R2, we can go to infinity in as many directions as points have the circle. [...]
2023 - 10.3390/sym15081476
Symmetry, Vol. 15, Issue 8 (August 2023) , art. 1476
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On the "traveling pulses" of the limit of the FitzHugh-Nagumo equation when ɛ→0
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
A solution (u(s), v(s)) of the differential system u = v, v = −cv−u(u−a)(1−u) + w, w = −(ɛ/c)(u−γw) with a, c, ɛ ∈ R such that (u(s), v(s)) → (0,0) when s → ± ∞ is a traveling pulse of the FitzHugh-Nagumo equation. [...]
2023 - 10.1016/j.nonrwa.2023.103891
Nonlinear Analysis: Real World Applications, Vol. 73 (October 2023) , art. 103891
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14 p, 1.1 MB |
Planar Kolmogorov systems with infinitely many singular points at infinity
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Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. [...]
2022 - 10.1142/S0218127422500651
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 5 (April 2022) , art. 2250065
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71 p, 954.7 KB |
The hyperbolic Anderson model : moment estimates of the Malliavin derivatives and applications
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Balan, Raluca M. (University of Ottawa. Department of Mathematics and Statistics) ;
Nualart, David (University of Kansas. Department of Mathematics) ;
Quer i Sardanyons, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Zheng, Guangqu (The University of Edinburg. School of Mathematics)
In this article, we study the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension d= 1 , 2. Under mild assumptions, we provide Lp-estimates of the iterated Malliavin derivative of the solution in terms of the fundamental solution of the wave solution. [...]
2022 - 10.1007/s40072-021-00227-5
Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 10, Issue 3 (January 2022) , p. 757-827
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