Results 11 to 20 of about 172,487 (303)
Dependence of bacterial chemotaxis on gradient shape and adaptation rate.
PLoS Computational Biology, 2008 Simulation of cellular behavior on multiple scales requires models that are sufficiently detailed to capture central intracellular processes but at the same time enable the simulation of entire cell populations in a computationally cheap way.
Nikita Vladimirov +3 more
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Existence of solutions for singular quasilinear elliptic problems with dependence of the gradient
Electronic Journal of Qualitative Theory of Differential EquationsIn this paper we establish existence of solutions to the following boundary value problem involving a $p$-gradient term $$\displaystyle -\Delta_{p} u + g(u)|\nabla u|^p = \lambda u^\sigma+ \Psi(x), \quad u>0 \quad\mbox{in} ~\Omega, \quad u = 0 ...
Jose Gonçalves +3 more
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Multidimensional encoding of restricted and anisotropic diffusion by double rotation of the q vector [PDF]
Magnetic Resonance, 2023 Diffusion NMR and MRI methods building on the classic pulsed gradient spin-echo sequence are sensitive to many aspects of translational motion, including time and frequency dependence (“restriction”), anisotropy, and flow, leading to ambiguities when ...
H. Jiang, L. Svenningsson, D. Topgaard
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Gradient system with dependence on the gradient at nonlinearity [PDF]
Applied Mathematical Sciences, 2013 In this paper we establish existence of solutions for quasilinear elliptic system of gradient form with dependence on the gradient at nonlinearity.
Rua Gabriel Monteiro da Silva +1 more
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Singular quasilinear convective elliptic systems in ℝN
Advances in Nonlinear Analysis, 2022 The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates.
Guarnotta Umberto +2 more
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The $p$-weak gradient depends on $p$ [PDF]
Proceedings of the American Mathematical Society, 2015 Given a>0, we construct a weighted Lebesgue measure on R^n for which the family of non constant curves has p-modulus zero for p\leq 1+a but the weight is a Muckenhoupt A_p weight for p>1+a. In particular, the p-weak gradient is trivial for small p but non trivial for large p. This answers an open question posed by several authors.
di Marino S., Speight G.
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On the relaxation of integral functionals depending on the symmetrized gradient [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020 AbstractWe prove results on the relaxation and weak* lower semicontinuity of integral functionals of the form$${\cal F}[u]: = \int_\Omega f \left( {\displaystyle{1 \over 2}\left( {\nabla u(x) + \nabla u{(x)}^T} \right)} \right) \,{\rm d}x,\quad u:\Omega \subset {\mathbb R}^d\to {\mathbb R}^d,$$over the space BD(Ω) of functions of bounded deformation or
Kosiba, Kamil, Rindler, Filip
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Some recent results on singular p-Laplacian equations
Demonstratio Mathematica, 2022 A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions.
Guarnotta Umberto +2 more
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A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
Mathematics, 2020 The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems.
Dumitru Motreanu +2 more
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Gradient estimates for nonlinear elliptic equations with a gradient-dependent nonlinearity [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2019 AbstractIn this paper, we obtain gradient estimates of the positive solutions to weightedp-Laplacian type equations with a gradient-dependent nonlinearity of the form0.1$${\rm div }( \vert x \vert ^\sigma \vert \nabla u \vert ^{p-2}\nabla u) = \vert x \vert ^{-\tau }u^q \vert \nabla u \vert ^m\quad {\rm in}\;\Omega^*: = \Omega {\rm \setminus }\{ 0\} .$$
Joshua Ching, Florica C. Cîrstea
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