Results 31 to 40 of about 17,298,525 (250)
Well posedness of the nonlinear Schrödinger equation with isolated singularities [PDF]
Journal of Differential Equations, 2020 We study the well posedness of the nonlinear Schrödinger (NLS) equation with a point interaction and power nonlinearity in dimension two and three. Behind the autonomous interest of the problem, this is a model of the evolution of so called singular ...
C. Cacciapuoti, D. Finco, D. Noja
semanticscholar +1 more source
The Jordan–Moore–Gibson–Thompson Equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time [PDF]
Mathematical Models and Methods in Applied Sciences, 2019 In this paper, we consider the Jordan–Moore–Gibson–Thompson equation, a third-order in time wave equation describing the nonlinear propagation of sound that avoids the infinite signal speed paradox of classical second-order in time strongly damped models
B. Kaltenbacher, Vanja Nikoli'c
semanticscholar +1 more source
Tykhonov well-posedness of split problems
Journal of Inequalities and Applications, 2020 In (J. Optim. Theory Appl. 183:139–157, 2019) we introduced and studied the concept of well-posedness in the sense of Tykhonov for abstract problems formulated on metric spaces. Our aim of this current paper is to extend the results in (J. Optim.
Qiao-yuan Shu +2 more
doaj +1 more source
On differentiability in the Wasserstein space and well-posedness for Hamilton–Jacobi equations
Journal des Mathématiques Pures et Appliquées, 2019 In this paper we elucidate the connection between various notions of differentiability in the Wasserstein space: some have been introduced intrinsically (in the Wasserstein space, by using typical objects from the theory of Optimal Transport) and used by
W. Gangbo, A. Tudorascu
semanticscholar +1 more source
On the Well-posedness of Bayesian Inverse Problems [PDF]
SIAM/ASA J. Uncertain. Quantification, 2019 The subject of this article is the introduction of a weaker concept of well-posedness of Bayesian inverse problems. The conventional concept of (`Lipschitz') well-posedness in [Stuart 2010, Acta Numerica 19, pp.
J. Latz
semanticscholar +1 more source
On some variational inequality-constrained control problems
Journal of Inequalities and Applications, 2022 In this paper, by considering some properties associated with scalar functionals of multiple-integral type, we study the well-posedness and generalized well-posedness for a new variational inequality-constrained optimization problems By using the set of ...
Savin Treanţă +2 more
doaj +1 more source
SIAM Review, 2020 This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is coupled with a static or time-varying set-valued operator in the feed...
B. Brogliato, A. Tanwani
semanticscholar +1 more source
Well-posedness and numerical algorithm for the tempered fractional differential equations
Discrete & Continuous Dynamical Systems - B, 2019 Trapped dynamics widely appears in nature, e.g., the motion of particles in viscous cytoplasm. The famous continuous time random walk (CTRW) model with power law waiting time distribution (having diverging first moment) describes this phenomenon. Because
Can Li, W. Deng, Lijing Zhao
semanticscholar +1 more source
Well-posedness of distribution dependent SDEs with singular drifts [PDF]
Bernoulli, 2018 In this paper we consider the following distribution dependent SDE: $$ {\mathrm d} X_t=\sigma_t(X_t,\mu_{X_t}){\mathrm d} W_t+b_t(X_t,\mu_{X_t}){\mathrm d} t, $$ where $\mu_{X_t}$ stands for the distribution of $X_t$. We show the strong well-posedness of
M. Rockner, Xicheng Zhang
semanticscholar +1 more source
On unconditional well-posedness of modified KdV [PDF]
, 2011 Bourgain(1993) proved that the periodic modified KdV equation (mKdV) is locally well-posed in Sobolev spave H^s(T), s >= 1/2, by introducing new weighted Sobolev spaces X^s,b, where the uniqueness holds conditionally, namely in the intersection of C([0 ...
Babin +15 more
core +2 more sources