Efficient computation of delay differential equations with highly oscillatory terms. [PDF]
, 2012 This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory forcing terms.
Condon, Marissa +3 more
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Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution
Proceedings of the National Academy of Sciences of the United States of America, 2021 Significance Using computational modeling, we designed a self-oscillating materials system that is driven by a nonperiodic chemical reaction to undergo both periodic shape changes and motion.
R. Manna, Oleg E. Shklyaev, A. Balazs
semanticscholar +1 more source
Long-Time Asymptotics of Perturbed Finite-Gap Korteweg-de Vries Solutions [PDF]
, 2012 We apply the method of nonlinear steepest descent to compute the long-time asymptotics of solutions of the Korteweg--de Vries equation which are decaying perturbations of a quasi-periodic finite-gap background solution.
A. B. d. Monvel +37 more
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Oscillatory Solutions for Certain Delay-Differential Equations [PDF]
Proceedings of the American Mathematical Society, 1988 The existence of oscillatory solutions for a certain class of scalar first order delay-differential equations is proved. An application to a delay logistic equation arising in certain models for population variation of a single specie in a constant environment with limited resources for growth is considered.
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Oscillatory Solutions of Singular Equations Arising in Hydrodynamics [PDF]
Advances in Difference Equations, 2010 Motivated by the recent papers of the first two authors [Math. Comput. Modelling 51, No.~5--6, 658--669 (2010; Zbl 1190.34029), and Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No.~3--4 (A), 2114--2118 (2010; Zbl 1186.34014)], the initial value problem for the second order nonlinear differential equation \[ (p(t)u')'=p(t)f(u),\quad
Rachůnková, Irena +2 more
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Dynamical Instabilities of Quasi-static Crack Propagation Under Thermal Stress [PDF]
, 2003 We address the theory of quasi-static crack propagation in a strip of glass that is pulled from a hot oven towards a cold bath. This problem had been carefully studied in a number of experiments that offer a wealth of data to challenge the theory.
Bouchbinder, Eran +2 more
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Oscillatory traveling wave solutions for coagulation equations
Quarterly of Applied Mathematics, 2017 We consider Smoluchowski's coagulation equation with kernels of homogeneity one of the form $K_{\varepsilon }( , ) =\big( ^{1-\varepsilon }+ ^{1-\varepsilon }\big)\big ( \big) ^{\frac{\varepsilon }{2}}$. Heuristically, in suitable exponential variables, one can argue that in this case the long-time behaviour of solutions is similar to the ...
Niethammer, B., Velázquez, J. J. L.
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Oscillatory Solutions of Neutral Equations with Polynomial Nonlinearities [PDF]
International Journal of Differential Equations, 2011 Existence uniqueness of an oscillatory solution for nonlinear neutral equations by fixed point method is proved.
Angelov, Vasil G., Angelova, Dafinka Tz.
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Oscillation of solutions to non-linear difference equations with several advanced arguments [PDF]
Opuscula Mathematica, 2017 This work concerns the oscillation and asymptotic properties of solutions to the non-linear difference equation with advanced arguments \[x_{n+1}- x_n =\sum_{i=1}^m f_{i,n}( x_{n+h_{i,n}}).\] We establish sufficient conditions for the existence of ...
Sandra Pinelas, Julio G. Dix
doaj +1 more source
Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on $T^3 \times R$ [PDF]
, 1998 A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$.
A. A. Kirillov +40 more
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