Weakly coupled systems of semilinear σ‐evolution equations with friction and visco‐elastic type damping
Sign Up to like & getrecommendations! Published in 2024 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.10473
Abstract: In the present paper, we are interested to study global (in time) existence of small data Sobolev solutions to the Cauchy problem for a weakly coupled system of two semilinear σk$$ {\sigma}_k $$ ‐evolution equations… read more here.
Keywords: x0005e; equations friction; weakly coupled; amp x0005e ... See more keywords
Remarks on Semilinear σ‐Evolution Equations With Critical Damping and Critical Nonlinearity of Derivative Type
Sign Up to like & getrecommendations! Published in 2025 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.11155
Abstract: In this article, we indicate that under suitable assumptions of a modulus of continuity, we obtain either the global (in time) existence of small data Sobolev solutions or the blow‐up result of local (in time)… read more here.
Keywords: derivative type; nonlinearity derivative; evolution equations;
Two-loop evolution equations for flavor-singlet light-ray operators
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep02(2019)191
Abstract: A bstractQCD in non-integer d = 4 − 2ϵ space-time dimensions enjoys conformal invariance at the special fine-tuned value of the coupling. Counterterms for composite operators in minimal subtraction schemes do not depend on ϵ… read more here.
Keywords: light ray; flavor singlet; evolution equations; two loop ... See more keywords
Almost automorphic solutions for nonautonomous parabolic evolution equations
Sign Up to like & getrecommendations! Published in 2019 at "Semigroup Forum"
DOI: 10.1007/s00233-019-10045-w
Abstract: In this work, we study the existence and uniqueness of almost automorphic solutions for semilinear nonautonomous parabolic evolution equations with inhomogeneous boundary conditions using the exponential dichotomy. We assume that the homogeneous problem satisfies the… read more here.
Keywords: automorphic solutions; parabolic evolution; evolution equations; nonautonomous parabolic ... See more keywords
Randomness and Nonlinear Evolution Equations
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-019-8297-5
Abstract: In this paper we survey some results on existence, and when possible also uniqueness, of solutions to certain evolution equations obtained by injecting randomness either on the set of initial data or as a perturbative… read more here.
Keywords: randomness nonlinear; evolution; evolution equations; nonlinear evolution ... See more keywords
Regularity of the Inertial Manifolds for Evolution Equations in Admissible Spaces and Finite-Dimensional Feedback Controllers
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-021-09538-1
Abstract: Our main aims in this paper are to investigate the regularity of inertial manifolds for non-autonomous semi-linear evolution equations and to give an application of inertial manifolds to a feedback control problem. We first prove… read more here.
Keywords: evolution equations; regularity inertial; equations admissible; manifolds evolution ... See more keywords
Setvalued Dynamical Systems for Stochastic Evolution Equations Driven by Fractional Noise
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-019-09811-9
Abstract: We consider Hilbert-valued evolution equations driven by Hölder paths with Hölder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2,1). The assumptions of the drift term will not… read more here.
Keywords: evolution equations; dynamical systems; dynamical system; setvalued dynamical ... See more keywords
Localized solutions of (5+1)-dimensional evolution equations
Sign Up to like & getrecommendations! Published in 2021 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-021-06541-w
Abstract: In this research, the general linear evolution equations (EEs) in (5+1) dimensions are studied. All the mixed second-order derivatives are included in this aforementioned model. Using the Hirota bilinear operator and symbolic computation, the localized… read more here.
Keywords: solutions dimensional; localized solutions; abundant lump; lump solutions ... See more keywords
An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Pseudo-Differential Operators and Applications"
DOI: 10.1007/s11868-025-00733-3
Abstract: We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This formulation is applicable to evolution equations involving… read more here.
Keywords: logarithmic laplacian; evolution equations; second order; pseudo differential ... See more keywords
Existence and Regularity of q-Mild Solutions to Fractional Evolution Equations with Noncompact Semigroups
Sign Up to like & getrecommendations! Published in 2018 at "Differential Equations and Dynamical Systems"
DOI: 10.1007/s12591-016-0337-3
Abstract: We discuss the existence and regularity of solutions to some fractional evolution equations in the q-norm. The linear part generates a noncompact semigroup, and the nonlinear part satisfies some conditions with respect to the fractional… read more here.
Keywords: evolution equations; existence regularity; fractional evolution; solutions fractional ... See more keywords
Complex symmetric evolution equations
Sign Up to like & getrecommendations! Published in 2019 at "Analysis and Mathematical Physics"
DOI: 10.1007/s13324-020-00358-3
Abstract: We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a $$\mathcal {C}$$… read more here.
Keywords: mathcal selfadjoint; symmetric evolution; evolution equations; complex symmetric ... See more keywords