Results 61 to 70 of about 14,488 (245)

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

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

SOME MIXED PROBLEMS FOR SEMILINEAR PARABOLIC TYPE EQUATION

Journal of Applied Analysis & Computation, 2014
In this paper, some mixed problem with third type boundary value for a semilinear parabolic equation is investigated. Here the solvability theorems for considered problem and the uniqueness theorem for a model case of the problem are showed.
Duzgun, Fatma Gamze, Soltanov, Kamal
openaire   +2 more sources

A cell complex structure for the space of heteroclines for a semilinear parabolic equation

Electronic Journal of Differential Equations, 2009
It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells.
Michael Robinson
doaj  

Existence and Uniqueness of Nonmonotone Solutions in Porous Media Flow

Axioms, 2022
Existence and uniqueness of solutions for a simplified model of immiscible two-phase flow in porous media are obtained in this paper. The mathematical model is a simplified physical model with hysteresis in the flux functions.
Rouven Steinle, Tillmann Kleiner, Pradeep Kumar, Rudolf Hilfer   +3 more
doaj   +1 more source

Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in $R^n$

, 2016
We prove the boundedness of global classical solutions for the semilinear heat equation $u_t-\Delta u= |u|^{p-1}u$ in the whole space $R^n$, with $n\ge 3$ and supercritical power $p>(n+2)/(n-2)$.
Adams, Biler, Blatt, Blatt, Blatt, Cazenave, Chen, Chou, Fila, Fila, Fila, Galaktionov, Galaktionov, Giga, Giga, Giga, Giga, Haraux, Karch, Kato, Kavian, Kawanago, Kozono, Lee, Lemarié-Rieusset, Matano, Matano, Matano, Mizoguchi, Mizoguchi, Ni, Ortner, Otani, Pacard, Philippe Souplet, Poláčik, Poláčik, Poláčik, Quittner, Quittner, Quittner, Snoussi, Souplet, Souplet, Souplet, Taylor, Triebel, Weissler, Yamazaki   +48 more
core   +3 more sources

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

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

Blowup of solutions of semilinear parabolic equations

Journal of Mathematical Analysis and Applications, 1988
Consider the blow-up behavior of solutions of a semilinear parabolic equation \[ (1)\quad u_ t+uu_ x-u_{xx}=f(u)\quad (-a0)\), \(u(x,0)=\phi (x ...
Friedman, Avner, Lacey, Andrew A
openaire   +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