Results 1 to 10 of about 1,718,820 (284)
Dynamical extensions for shell-crossing singularities
, 2003 We derive global weak solutions of Einstein's equations for spherically symmetric dust-filled space-times which admit shell-crossing singularities. In the marginally bound case, the solutions are weak solutions of a conservation law.
Brien C Nolan +25 more
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Weak solutions for a strongly-coupled nonlinear system
Electronic Journal of Differential Equations, 2006 In this paper the authors study the existence of local weak solutions of the strongly nonlinear system $$displaylines{ u''+mathcal{A}u +f(u,v)u = h_1 cr v''+mathcal{A}v +g(u,v)v = h_2 }$$ where $mathcal{A}$ is the pseudo-Laplacian operator and $f$, $g$, $
Osmundo A. Lima +2 more
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Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet forms [PDF]
, 2016 In the context of a metric measure Dirichlet space satisfying volume doubling and Poincar\'e inequality, we prove the parabolic Harnack inequality for weak solutions of the heat equation associated with local nonsymmetric bilinear forms.
Lierl, Janna, Saloff-Coste, Laurent
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Weak solutions for weak turbulence models in electrostatic plasmas
, 2023 The weak turbulence model, also known as the quasilinear theory in plasma physics, has been a cornerstone in modeling resonant particle-wave interactions in plasmas. This reduced model stems from the Vlasov-Poisson/Maxwell system under the weak turbulence assumption, incorporating the random phase approximation and ergodicity.
Huang, Kun, Gamba, Irene M.
openaire +2 more sources
On asymptotic behavior of global solutions for hyperbolic hemivariational inequalities
Electronic Journal of Differential Equations, 2006 In this paper we study the existence of global weak solutions for a hyperbolic differential inclusion with a discontinuous and nonlinear multi-valued term. Also we investigate the asymptotic behavior of solutions.
Jong Yeoul Park, Sun Hye Park
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Weak solutions for parabolic equations with p(x)-growth
Electronic Journal of Differential Equations, 2016 In this article we study nonlinear parabolic equations with p(x)-growth in the space $W^{1,x}L^{p(x)}(Q)\cap L^\infty(0,T; L^2(\Omega))$. By using the method of parabolic regularization, we prove the existence and uniqueness of weak solutions for the
Ning Pan, Binlin Zhang, Jun Cao
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On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions \begin{equation*} \begin{cases} -\mathcal{L}_{K}u=\lambda f(x,u), &
Qing-Mei Zhou
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Weak solutions for a viscous p-Laplacian equation
Electronic Journal of Differential Equations, 2003 In this paper, we consider the pseudo-parabolic equation $ u_t-kDelta u_t=mathop{ m div}(| abla u|^{p-2} abla u)$. By using the time-discrete method, we establish the existence of weak solutions, and also discuss the uniqueness.
Changchun Liu
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AxiomsA system of nonlinear wave equations in viscoelasticity with variable exponents is considered. It is assumed that the kernel included in the integral term of the equations depends on both the time and the spatial variables.
Mouhssin Bayoud +4 more
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The Poisson equation from non-local to local
Electronic Journal of Differential Equations, 2018 We analyze the limiting behavior as $s\to 1^-$ of the solution to the fractional Poisson equation $(-\Delta)^s{u_s}=f_s$, $x\in\Omega$ with homogeneous Dirichlet boundary conditions $u_s\equiv 0$, $x\in\Omega^c$. We show that $\lim_{s\to 1^-} u_s =u$,
Umberto Biccari +1 more
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