Results 51 to 60 of about 240 (185)

On the principle of linearized stability for quasilinear evolution equations in time‐weighted spaces

Mathematische Nachrichten, Volume 298, Issue 12, Page 3939-3959, December 2025.
Abstract Quasilinear (and semilinear) parabolic problems of the form v′=A(v)v+f(v)$v^{\prime }=A(v)v+f(v)$ with strict inclusion dom(f)⊊dom(A)$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function v↦f(v)$v\mapsto f(v)$ and the quasilinear part v↦A(v)$v\mapsto A(v)$ are considered in the framework of time‐weighted function spaces ...
Bogdan‐Vasile Matioc, Lina Sophie Schmitz, Christoph Walker   +2 more
wiley   +1 more source

Quasilinear Degenerate Evolution Systems Modelling Biofilm Growth: Well‐Posedness and Qualitative Properties

Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.
ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
wiley   +1 more source

Global attractor for a semilinear parabolic equation involving Grushin operator

Electronic Journal of Differential Equations, 2008
The aim of this paper is to prove the existence of a global attractor for a semilinear degenerate parabolic equation involving the Grushin operator.
Phan Quoc Hung, Tran Dinh Ke, Trinh Tuan Phong, Cung The Anh   +3 more
doaj  

Multidimensional Stability of Planar Traveling Waves for Stochastically Perturbed Reaction–Diffusion Systems

Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.
ABSTRACT We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales ...
M. van den Bosch, H. J. Hupkes
wiley   +1 more source

Blow-up Criteria for Semilinear Parabolic Equations

Journal of Mathematical Analysis and Applications, 2000
The authors consider initial boundary value problems for the semilinear equation \(u_t-\Delta u=f(u)\) with \(C_0(\overline\Omega)\) initial data and zero data on the boundary. The nonlinearity \(f\in C^1\) supposed to be a convex function. they prove blow-up criteria based on the construction of super- and sub-solutions for the problem under ...
Kohda, Atsuhito, Suzuki, Takashi
openaire   +3 more sources

Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7609-7629, 15 May 2025.
This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ...
Vicente J. Bevia, Juan C. Cortés, Rafael J. Villanueva   +2 more
wiley   +1 more source

Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition

Electronic Journal of Qualitative Theory of Differential Equations, 2010
In this paper, we consider a semilinear parabolic equation $$u_t=\Delta u+u^q\int_0^tu^p(x,s)ds,\quad x\in \Omega,\quad t>0$$ with nonlocal nonlinear boundary condition $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omega\varphi(x,y) u^l(y,t)dy$ and ...
Dengming Liu, Chunlai Mu
doaj   +1 more source

A Non‐Intrusive, Online Reduced Order Method for Non‐Linear Micro‐Heterogeneous Materials

International Journal for Numerical Methods in Engineering, Volume 126, Issue 5, 15 March 2025.
ABSTRACT In this contribution we present an adaptive model order reduction technique for non‐linear finite element computations of micro‐heterogeneous materials. The presented projection‐based method performs updates of the reduced basis during the iterative process and at the end of each load step.
Yasemin von Hoegen, Rainer Niekamp, Jörg Schröder   +2 more
wiley   +1 more source

Degenerate semilinear parabolic equations

Differential and Integral Equations, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Approximate controllability for fractional semilinear parabolic equations

Computers & Mathematics with Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Yong, Liu, Zhenhai, Wen, Ching-Feng   +2 more
openaire   +2 more sources