Results 61 to 70 of about 12,988 (199)

Existence of extremal periodic solutions for quasilinear parabolic equations

Abstract and Applied Analysis, 1997
In this paper we consider a quasilinear parabolic equation in a bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately ...
Siegfried Carl
doaj   +1 more source

Potential estimates and quasilinear parabolic equations with measure data [PDF]

, 2014
In this paper, we study the existence and regularity of the quasilinear parabolic equations: $$u_t-\text{div}(A(x,t,\nabla u))=B(u,\nabla u)+\mu$$ in $\mathbb{R}^{N+1}$, $\mathbb{R}^N\times(0,\infty)$ and a bounded domain $\Omega\times (0,T)\subset ...
Quoc-hung Nguyen, See Profile
core   +7 more sources

Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem

, 2013
In this work we consider the identifiability of two coefficients $a(u)$ and $c(x)$ in a quasilinear elliptic partial differential equation from observation of the Dirichlet-to-Neumann map.
Egger, Herbert, Pietschmann, Jan-Frederik, Schlottbom, Matthias   +2 more
core   +1 more source

Maximum principle for the weak solutions of the Cauchy problem for the fourth‐order hyperbolic equations

PAMM, 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

Entropy solutions of forward-backward parabolic equationswith Devonshire free energy

Networks and Heterogeneous Media, 2012
A class of quasilinear parabolic equations offorward-backward type $u_t=[\phi(u)]_{xx}$ in one space dimension is addressed, under assumptions on thenonlinear term $\phi$ which hold for a number of mathematical models in the theory of phase transitions.
Flavia Smarrazzo, Alberto Tesei
doaj   +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, Runan He, Andrew A. Lacey   +2 more
wiley   +1 more source

Expanding solutions of quasilinear parabolic equations

Communications on Pure and Applied Analysis, 2021
By using the theory of maximal $L^{q}$-regularity and methods of singular analysis, we show a Taylor's type expansion--with respect to the geodesic distance around an arbitrary point--for solutions of quasilinear parabolic equations on closed manifolds. The powers of the expansion are determined explicitly by the local geometry, whose reflection to the
openaire   +4 more sources

A duality for prescribed mean curvature graphs in Riemannian and Lorentzian Killing submersions

Mathematische Nachrichten, Volume 297, Issue 5, Page 1581-1600, May 2024.
Abstract We develop a conformal duality for space‐like graphs in Riemannian and Lorentzian three‐manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is time‐like in the Lorentzian case.
Andrea Del Prete, Hojoo Lee, José Miguel Manzano   +2 more
wiley   +1 more source

The Mullins–Sekerka problem via the method of potentials

Mathematische Nachrichten, Volume 297, Issue 5, Page 1960-1977, May 2024.
Abstract It is shown that the two‐dimensional Mullins–Sekerka problem is well‐posed in all subcritical Sobolev spaces Hr(R)$H^r({\mathbb {R}})$ with r∈(3/2,2)$r\in (3/2,2)$. This is the first result, where this issue is established in an unbounded geometry.
Joachim Escher, Anca‐Voichita Matioc, Bogdan‐Vasile Matioc   +2 more
wiley   +1 more source

Directed mean curvature flow in noisy environment

Communications on Pure and Applied Mathematics, Volume 77, Issue 3, Page 1850-1939, March 2024.
Abstract We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole–Hopf solution of the KPZ equation.
Andris Gerasimovičs, Martin Hairer, Konstantin Matetski   +2 more
wiley   +1 more source