Applied Mathematics Letters, 2021 We establish the local existence and uniqueness of weak solutions for fractional pseudo-parabolic equation with singular potential by means of Galerkin method and contraction mapping theorem.
Zhong Tan, Minghong Xie, Zhonger Wu
exaly +2 more sources
Local Existence of Solutions to the Initial-Value Problem for One-Dimensional Strain-Limiting Viscoelasticity [PDF]
Journal of Differential Equations, 2020 In this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of ...
Yasemin Sengül, Albert Erkip, H A Erbay
exaly +2 more sources
Local and Global Existence Theorems for the Einstein Equations
Living Reviews in Relativity, 2000 This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first.
Rendall Alan D.
doaj +2 more sources
Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity [PDF]
Opuscula Mathematica, 2023 This paper concerns a viscoelastic Kirchhoff-type equation with the dispersive term, internal damping, and logarithmic nonlinearity. We prove the local existence of a weak solution via a modified lemma of contraction of the Banach fixed-point theorem ...
Sebastião Cordeiro +4 more
doaj +1 more source
Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms [PDF]
Theoretical and Applied Mechanics, 2020 In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions 𝜛𝑖, (𝑖 = 1, 2),
Pişkin Erhan +2 more
doaj +1 more source
Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence [PDF]
Nonlinearity, 2020 In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear ...
A. Agresti, M. Veraar
semanticscholar +1 more source
Communications on Pure and Applied Analysis, 2021 In this manuscript, we study the theory of conformal relativistic viscous hydrodynamics introduced in [ 4 ], which provided a causal and stable first-order theory of relativistic fluids with viscosity.
F. S. Bemfica +3 more
semanticscholar +1 more source
Local existence of analytic sharp fronts for singular SQG [PDF]
Nonlinear Analysis, 2020 In this paper, we prove local existence and uniqueness of analytic sharp-front solutions to a generalised SQG equation by the use of an abstract Cauchy--Kowalevskaya theorem. Here, the velocity is determined by $u = |\nabla|^{-2\beta}\nabla^\perp\theta $
Calvin Khor, José L. Rodrigo
semanticscholar +1 more source
On regular solutions to compressible radiation hydrodynamic equations with far field vacuum
Advances in Nonlinear Analysis, 2022 The Cauchy problem for three-dimensional (3D) isentropic compressible radiation hydrodynamic equations is considered. When both shear and bulk viscosity coefficients depend on the mass density ρ\rho in a power law ρδ{\rho }^{\delta } (with ...
Li Hao, Zhu Shengguo
doaj +1 more source
Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type
Open Mathematics, 2023 The Cauchy problem in Rn{{\mathbb{R}}}^{n}, n≥2n\ge 2, for ut=Δu−∇⋅(uS⋅∇v),0=Δv+u,(⋆)\begin{array}{r}\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}_{t}=\Delta u-\nabla \cdot \left(uS\cdot \nabla v),\\ 0=\Delta v+u,\end{array}\right.\hspace{2 ...
Winkler Michael
doaj +1 more source