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Sensitivity equations for measure-valued solutions to transport equations
(American Institute of Mathematical Sciences, 2020-01)
We consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, ...
Fractional calculus for differential equationsCálculo fraccionario para ecuaciones diferenciales
(USFQ PRESS, departamento editorial de la Universidad San Francisco de Quito USFQ, 2021)
A repulsive interaction in the classical electrodynamics
(Budapest Tech, 2020-01)
Herein, we introduce an additional term into the induction equation (one of the Maxwell’s equation). The related Lagrangian formalism applying the scalar and vector potentials is fitted to this modified Maxwell’s equations. ...
Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems
(Springer/Plenum Publishers, 2011-02)
Partial differential equations for the unknown final state and initial costate arising in the Hamiltonian formulation of regular optimal control problems with a quadratic final penalty are found. It is shown that the missing ...
Variational Principles for Lie-Poisson and Hamilton-Poincaré Equations
(Independent Univ Moscow, 2003-07)
As is well-known, there is a variational principle for theEuler–Poincar ́e equations on a Lie algebragof a Lie groupGobtainedby reducing Hamilton’s principle onGby the action ofGby, say, leftmultiplication. The purpose of ...
Existence of ground states for a one-dimensional relativistic schrödinger equation
(American Institute of Physics, 2012-06)
Relativistic Schrödinger equation with a nonlinear potential interaction describes the dynamics of a particle, with rest mass m, travelling to a significant fraction |v| < 1 of the light speed c = 1. At first, we deal with ...
Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions
(American Institute of Mathematical Sciences, 2021-07)
We study the decay/growth rates in all Lp norms of solutions to an inhomogeneousnonlocal heat equation in RN involving a Caputo -time derivative and a power of the Laplacianwhen the dimension is large, N > 4. Rates depend ...
Diffusive limit to a selection-mutation equation with small mutation formulated on the space of measures
(American Institute of Mathematical Sciences, 2021-03)
In this paper we consider a selection-mutation model with an advection term formulated on the space of finite signed measures on Rd. The selection-mutation kernel is described by a family of measures which allows the study ...
The homotopy analysis method in bifurcation analysis of delay differential equations
(World Scientific, 2012-05)
In this paper we apply the homotopy analysis method (HAM) to study the van der Pol equation with a linear delayed feedback. The paper focuses on the calculation of periodic solutions and associated bifurcations, Hopf, ...
Time–space white noise eliminates global solutions in reaction–diffusion equations
(Elsevier Science, 2009-01)
We prove that perturbing the reactiondiffusion equation ut = uxx + (u+) p p > 1), with timespace white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model ...