Results 51 to 60 of about 243 (185)

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

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

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

Construction of entire solutions for semilinear parabolic equations

Electronic Journal of Differential Equations, 2008
Entire solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one entire solution - the trivial solution.
Michael Robinson
doaj  

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

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

Semilinear Parabolic Equations on the Heisenberg Group with a Singular Potential

Abstract and Applied Analysis, 2012
We discuss the asymptotic behavior of solutions for semilinear parabolic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy's inequality, and the nonlinearity is controlled by Sobolev's inequality. We also
Houda Mokrani, Fatimetou Mint Aghrabatt
doaj   +1 more source

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

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

Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions

Journal of Applied Mathematics, 2013
We study exponential attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains. First, we give the existence of the exponential attractor in by proving that the corresponding semigroup satisfies the enhanced ...
Zhao-hui Fan
doaj   +1 more source