Zobrazeno 1 - 10
of 362
pro vyhledávání: '"P. Divyang"'
The study of low regularity Cauchy data for nonlinear dispersive PDEs has successfully been achieved using modulation spaces $M^{p,q}$ in recent years. In this paper, we study the inhomogeneous nonlinear Schr\"odinger equation (INLS) $$iu_t + \Delta
Externí odkaz:
http://arxiv.org/abs/2410.00869
We study Cauchy problem for the Hardy-H\'enon parabolic equation with an inverse square potential, namely, \[\partial_tu -\Delta u+a|x|^{-2} u= |x|^{\gamma} F_{\alpha}(u),\] where $a\ge-(\frac{d-2}{2})^2,$ $\gamma\in \mathbb R$, $\alpha>1$ and $F_{\a
Externí odkaz:
http://arxiv.org/abs/2407.13085
Autor:
Bhimani, Divyang G., Dalai, Rupak K.
We completely characterize the weighted Lebesgue spaces on the torus $\mathbb T^n$ and waveguide manifold $\mathbb T^n \times \mathbb R^m$ for which the solutions of the heat equation converge pointwise (as time tends to zero) to the initial data. In
Externí odkaz:
http://arxiv.org/abs/2406.14271
Autor:
Doshi, Divyang, Kim, Jung-Eun
In this research, we propose an innovative method to boost Knowledge Distillation efficiency without the need for resource-heavy teacher models. Knowledge Distillation trains a smaller ``student'' model with guidance from a larger ``teacher'' model,
Externí odkaz:
http://arxiv.org/abs/2404.09886
Autor:
Bhimani, Divyang G.
Modulation spaces have received considerable interest recently as it is the natural function spaces to consider low regularity Cauchy data for several nonlinear evolution equations. We establish global well-posedness for 3D Klein-Gordon-Hartree equat
Externí odkaz:
http://arxiv.org/abs/2307.11456
Autor:
Bhimani, Divyang G., Haque, Saikatul
We have established (a weak form of) ill-posedness for the KdV-Burgers equation on a real line in Fourier amalgam spaces $\widehat{w}_s^{p,q}$ with $s<-1$. The particular case $p=q=2$ recovers the result of L. Molinet and F. Ribaud [Int. Math. Res. N
Externí odkaz:
http://arxiv.org/abs/2307.10599
Complex optimal design and control processes often require repeated evaluations of expensive objective functions and consist of large design spaces. Data-driven surrogates such as neural networks and Gaussian processes provide an attractive alternati
Externí odkaz:
http://arxiv.org/abs/2307.03286
Autor:
Bhimani, Divyang, Toft, Joachim
We deduce factorization properties for a quasi-Banach module over a quasi-Banach algebra. Especially we extend a result by Hewitt and prove that if any such algebra which possess a bounded left approximate identity, then any element in the module can
Externí odkaz:
http://arxiv.org/abs/2307.01590
We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity. Our main contributions are as follows: -We establish the local well-posedness in Orlicz spaces. -By considering small in
Externí odkaz:
http://arxiv.org/abs/2306.02828
We prove local and global well-posedness for mixed fractional Hartree equation with low regularity Cauchy data in Fourier amalgam $\widehat{w}^{p,q}$ and modulation $M^{p,q}$ spaces. Similar results also hold for the Hartree equation with harmonic po
Externí odkaz:
http://arxiv.org/abs/2302.10683