The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems
Mathematics, 2022 In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we ...
Calogero Vetro
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On local existence of MHD contact discontinuities [PDF]
Discrete and Continuous Dynamical Systems - S, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
MORANDO, Alessandro +2 more
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A local existence result for Poincaré-Einstein metrics [PDF]
Advances in Mathematics, 2017 Given a closed Riemannian manifold $(M, g_M)$ of dimension $n \geq 3$, we prove the existence of a conformally compact Einstein metric $g_{+}$ defined on a collar neighborhood $M \times (0,1]$ whose conformal infinity is $[g_M]$.
M. Gursky, G'abor Sz'ekelyhidi
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Time dependent evolution inclusions governed by the difference of two subdifferentials
Electronic Journal of Qualitative Theory of Differential Equations, 2012 The purpose of this paper is to study evolution inclusions involving time dependent subdifferential operators which are non-monotone. More precisely, we study existence of solutions for the following evolution equation in a real Hilbert space $X$~: $u ...
S. Guillaume
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Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces [PDF]
Archive for Rational Mechanics and Analysis, 2016 This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts ...
C. Fefferman +3 more
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Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow [PDF]
, 2013 In this paper, we prove existence and uniqueness of measure solutions for the Cauchy problem associated to the (vectorial) continuity equation with a non-local ow.
Crippa, Gianluca +1 more
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Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions
Nonlinearity, 2018 In this paper, we study a diffusion model of Kirchhoff-type driven by a nonlocal integro-differential operator. As a particular case, we consider the following diffusion problem where [u]s is the Gagliardo seminorm of u, is a bounded domain with ...
Xiang Mingqi +2 more
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Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions [PDF]
, 2008 We establish new existence results for multiple positive solutions of fourth-order nonlinear equations which model deflections of an elastic beam. We consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non ...
J. R. L. Webb +5 more
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Quasi-Local Mass and the Existence of Horizons [PDF]
Communications in Mathematical Physics, 2007 In this paper, we obtain lower bounds for the Brown-York quasilocal mass and the Bartnik quasilocal mass for compact three manifolds with smooth boundaries. As a consequence, we derive sufficient conditions for the existence of horizons for a certain class of compact manifolds with boundary and some asymptotically flat complete manifolds.The method is ...
Shi, Yuguang, Tam, Luen-Fai
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Local existence and uniqueness for the non-resistive MHD equations in homogeneous Besov spaces [PDF]
, 2016 In the paper, we consider the Cauchy problem of the non-resistive MHD equations in homogeneous Besov spaces. We prove the local existence and uniqueness of the solution to the non-resistive MHD equations by using the iterative scheme and compactness ...
Jin-Lu Li, W. Tan, Zhao-Yang Yin
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