Results 11 to 20 of about 473 (57)
Uniqueness of conservative solutions for the Hunter-Saxton equation [PDF]
Res. Math. Sci. 9, 19 (2022), 2021 We show that the Hunter-Saxton equation $u_t+uu_x=\frac14\big(\int_{-\infty}^x d\mu(t,z)- \int^{\infty}_x d\mu(t,z)\big)$ and $\mu_t+(u\mu)_x=0$ has a unique, global, weak, and conservative solution $(u,\mu)$ of the Cauchy problem on the line.
arxiv +1 more source
A PDE approach of inflammatory phase dynamics in diabetic wounds
, 2014 The objective of the present paper is the modeling and analysis of the dynamics of macrophages and certain growth factors in the inammatory phase, the rst one of the wound healing process.
N. Cónsul, S. Oliva, M. Pellicer
semanticscholar +1 more source
, 2014 We consider damped linear hyperbolic equations with Dirichlet boundary conditions. We prove the existence, uniqueness, and regularity of the solution. We apply semi-discretization in time technique.
H. Bennour, M. S. Said
semanticscholar +1 more source
, 2013 To obtain existence and uniqueness when solving some nonlinear characteristic Cauchy problems, we define a special algebra GOM ( Ω ) of generalized functions on the closure Ω of an open set Ω in R constructed from the topological algebra OM ( Ω ) of ...
V. Dévoué +3 more
semanticscholar +1 more source
Classification of solutions to $Δu = u^{-γ}$ in the half-space [PDF]
arXiv, 2023 We provide a classification result for positive solutions to $\Delta u = u^{-\gamma}$ in the half space, under zero Dirichlet boundary condition.
arxiv
Advanced Nonlinear Studies, 2017 In the present paper we study the Dirichlet problem for an equation involving the 1-Laplacian and a total variation term as reaction.We prove a strong multiplicity result.
Abdellaoui Boumediene +2 more
doaj +1 more source
Global in time well-posedness of a three-dimensional periodic regularized Boussinesq system
Demonstratio MathematicaGlobal in time weak solution to a regularized periodic three-dimensional Boussinesq system is proved to exist in energy spaces. This solution depends continuously on the initial data. In particular, it is unique.
Almutairi Shahah
doaj +1 more source
On a nonlinear Robin problem with an absorption term on the boundary and L1 data
Advances in Nonlinear AnalysisWe deal with existence and uniqueness of nonnegative solutions to: −Δu=f(x),inΩ,∂u∂ν+λ(x)u=g(x)uη,on∂Ω,\left\{\begin{array}{ll}-\Delta u=f\left(x),\hspace{1.0em}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ \frac{\partial u}{\partial ...
Pietra Francesco Della +2 more
doaj +1 more source
On backward uniqueness for parabolic equations when Osgood continuity of the coefficients fails at one point [PDF]
arXiv, 2020 We prove uniqueness for backward parabolic equations whose coefficients are Osgood continuous in time for $t>0$ but not at $t=0$.
arxiv
An elementary proof of uniqueness of the particle trajectories for solutions of a class of shear-thinning non-Newtonian 2D fluids [PDF]
, 2012 We prove some regularity results for a class of two dimensional non-Newtonian fluids. By applying results from [Dashti and Robinson, Nonlinearity, 22 (2009), 735-746] we can then show uniqueness of particle trajectories.
arxiv +1 more source