Results 31 to 40 of about 18,832,328 (177)
Intrinsically Design‐Rule‐Compliant Nanophotonic Inverse Design via Learned Generative Manifolds
Laser &Photonics Reviews, EarlyView.A generative reparameterization framework for nanophotonic inverse design is introduced, restricting optimization to a learned manifold of design‐rule‐compliant geometries. Unlike conventional penalty‐based approaches, fabrication constraints are encoded intrinsically within the design representation.
Bahrem Serhat Danis +8 more
wiley +1 more source
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
wiley +1 more source
Well-posedness of nonlinear Schrödinger equations from deterministic and probabilistic viewpoints [PDF]
In this thesis, we study the Cauchy problem for nonlinear Schrödinger equations (NLS) in various settings. Firstly, we consider NLS with a quadratic nonlinearity |u|² on the two-dimensional torus.
Liu, Ruoyuan
core +1 more source
Two approaches for the stability of a nonlocal time-delayed fourth-order dispersive model
Kuwait Journal of Science, 2023 The primary concern of the current article is to investigate the well-posedness and stability problem of a nonlinear dispersive equation of order four and with a nonlocal time-delayed term.
Boumediène Chentouf
doaj +1 more source
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This paper focuses on optimal design problems in the context of the Kirchhoff‐Love model for pure bending of a thin, solid, symmetric plate under a transverse load. The objective is to simultaneously determine the optimal outer shape of the domain and the distribution of two isotropic materials within the domain in order to minimize compliance.
Ivana Crnjac +2 more
wiley +1 more source
Well-posedness and ill-posedness of the fifth-order modified KdV equation
Electronic Journal of Differential Equations, 2008 We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces. $$displaylines{ partial_t u - partial_x^5u + c_1partial_x^3(u^3) + c_2upartial_x upartial_x^2 u + c_3uupartial_x^3 u =0cr u(x,0)= u_0(x ...
Soonsik Kwon
doaj
On a strongly damped semilinear wave equation with time-varying source and singular dissipation
Advances in Nonlinear Analysis, 2022 This paper deals with the global well-posedness and blow-up phenomena for a strongly damped semilinear wave equation with time-varying source and singular dissipative terms under the null Dirichlet boundary condition.
Yang Yi, Fang Zhong Bo
doaj +1 more source
Fragmentation–Coagulation Processes With Advection or Diffusion in Space
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper, we consider a continuous fragmentation–coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of C0$$ {C}_0 $$‐semigroups with parameter and use them to show that the abstract Cauchy problem associated with a more ...
Jacek Banasiak, Nduduzo Majozi
wiley +1 more source
Stability of energy-critical nonlinear Schrodinger equations in high dimensions
Electronic Journal of Differential Equations, 2005 We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrodinger equations in dimensions $n geq 3$, for solutions which have large, but finite, energy and large, but finite, Strichartz norms ...
Terence Tao, Monica Visan
doaj
Algebra Properties in Fourier-Besov Spaces and Their Applications
Journal of Function Spaces, 2018 We estimate the norm of the product of two scale functions in Fourier-Besov spaces. As applications of these algebra properties, we establish the global well-posedness for small initial data and local well-posedness for large initial data of the ...
Xuhuan Zhou, Weiliang Xiao
doaj +1 more source