Results 71 to 80 of about 953 (219)
Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
Abstract and Applied Analysis, 2012 We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul)+uq, (x,t)∈RN×(0,T), where N≥1, p>2 , and m, l, q>1, and give a ...
Pan Zheng +4 more
doaj +1 more source
Codimension two mean curvature flow of entire graphs
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract We consider the graphical mean curvature flow of maps f:Rm→Rn$\mathbf {f}:{\mathbb {R}^{m}}\rightarrow {\mathbb {R}^{n}}$, m⩾2$m\geqslant 2$, and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well‐known maximum principle of Ecker ...
Andreas Savas Halilaj, Knut Smoczyk
wiley +1 more source
A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets [PDF]
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable ...
Ansgar Jüngel, Bertram Düring
core
Electronic Journal of Differential Equations, 2002 We present existence and stability results for periodic solutions of quasilinear parabolic equation related to Leray-Lions's type operators. To prove existence and localization, we use the penalty method; while for stability we use an approximation ...
Abderrahmane El Hachimi +1 more
doaj
Journal of Geophysical Research: Atmospheres, Volume 129, Issue 18, 28 September 2024.Abstract We present the first analysis of frame‐indifferent (objective) fluxes and material vortices in Large Eddy Simulations of atmospheric boundary layer turbulence. We extract rotating fluid features that maintain structural coherence over time for near‐neutral, transitional, and convective boundary layers.
Nikolas Aksamit +2 more
wiley +1 more source
Well-posedness and stationary solutions
, 2011 In this paper we prove existence and uniqueness of variational inequality solutions for a bistable quasilinear parabolic equation arising in the theory of solid-solid phase transitions and discuss its stationary solutions, which can be ...
Grinfeld, Michael, Burns, Martin
core
ON THE GLOBAL EXISTENCE OF SOLUTIONS TO QUASILINEAR PARABOLIC EQUATIONS [PDF]
Glasgow Mathematical Journal, 2004 The subject of the paper is the following quasilinear parabolic problem (P): \[ u_t - \text{div\,} (a(t,x,u) \nabla u) = f(t,x,u, \nabla u) \qquad \text{for} \quad t>0, \; x \in \Omega, \] \[ u(t,x) = 0 \quad \text{for} \quad t>0, \; x \in \partial \Omega, \qquad u(0,x) = \varphi (x) \quad \text{for} \quad x \in \bar \Omega.
openaire +1 more source
Proceedings in Applied Mathematics and Mechanics, Volume 24, Issue 1, June 2024.Abstract We investigate the maximum principle for the weak solutions to the Cauchy problem for the hyperbolic fourth‐order linear equations with constant complex coefficients in the plane bounded domain.
Kateryna Buryachenko
wiley +1 more source
Optimal control of the propagation of a graph in inhomogeneous media [PDF]
, 2009 We study an optimal control problem for viscosity solutions of a Hamilton–Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function.
Deckelnick, Klaus +5 more
core +1 more source
Existence and uniqueness for a coupled parabolic‐hyperbolic model of MEMS
Mathematical Methods in the Applied Sciences, Volume 47, Issue 7, Page 6310-6353, 15 May 2024.Local wellposedness for a nonlinear parabolic‐hyperbolic coupled system modeling Micro‐Electro‐Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has motion modeled by a semilinear hyperbolic equation.
Heiko Gimperlein +2 more
wiley +1 more source