Results 61 to 70 of about 240 (185)

Rectifiability, finite Hausdorff measure, and compactness for non‐minimizing Bernoulli free boundaries

Communications on Pure and Applied Mathematics, Volume 78, Issue 3, Page 545-591, March 2025.
Abstract While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time‐dependent ...
Dennis Kriventsov, Georg S. Weiss
wiley   +1 more source

Attractors for Nonautonomous Parabolic Equations without Uniqueness

International Journal of Differential Equations, 2010
Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the ...
Cung The Anh, Nguyen Dinh Binh
doaj   +1 more source

A nonlinear characterization of stochastic completeness of graphs

Mathematische Nachrichten, Volume 298, Issue 3, Page 925-943, March 2025.
Abstract We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem.
Marcel Schmidt, Ian Zimmermann
wiley   +1 more source

Existence of solutions to Burgers equations in a non-parabolic domain

Electronic Journal of Differential Equations, 2018
In this article, we study the semilinear Burgers equation with time variable coefficients, subject to boundary condition in a non-parabolic domain. Some assumptions on the boundary of the domain and on the coefficients of the equation will be imposed.
Yassine Benia, Boubaker-Khaled Sadallah
doaj  

Blow-up theorems of Fujita type for a semilinear parabolic equation with a gradient term

Advances in Difference Equations, 2018
This paper deals with the existence and non-existence of the global solutions to the Cauchy problem of a semilinear parabolic equation with a gradient term.
Yang Na, Mingjun Zhou, Xu Zhou, Guanming Gai   +3 more
doaj   +1 more source

Existence and continuity of global attractors for a degenerate semilinear parabolic equation

Electronic Journal of Differential Equations, 2009
In this article, we study the existence and the upper semicontinuity with respect to the nonlinearity and the shape of the domain of global attractors for a semilinear degenerate parabolic equation involving the Grushin operator.
Cung The Anh, Tran Dinh Ke
doaj  

Semilinear parabolic equations in $L^1(\Omega)$

Advances in Differential Equations, 2007
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openaire   +4 more sources

Semilinear evolution equations of the parabolic type [PDF]

Annales Polonici Mathematici, 1999
The author proves an existence and uniqueness result concerning classical solutions to a semilinear time-dependent differential equation in a real Banach space.
openaire   +1 more source

An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions

Electronic Journal of Differential Equations, 2001
In this paper we prove an approximate controllability result for an abstract semilinear evolution equation in a Hilbert space and we obtain as consequences the approximate controllability for some classes of elliptic and parabolic problems subjected to ...
Ioan Bejenaru, Jesus Ildefonso Diaz, Ioan I. Vrabie   +2 more
doaj  

Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition

Abstract and Applied Analysis, 2013
This work is concerned with a mixed boundary value problem for the semilinear parabolic equation with a memory term and generalized Lewis functions which depends on both spacial variable and time.
Zhong Bo Fang, Liru Qiu
doaj   +1 more source