Results 21 to 30 of about 15,308,767 (115)

Boundary value problems for semilinear evolution equations of compact type [PDF]

, 1982
Bibliography: p.
Sager, Herbert Casper
core   +1 more source

A nonlocal mixed semilinear problem for second-order hyperbolic equations

Electronic Journal of Differential Equations, 2003
In this work we study a nonlinear hyperbolic one-dimensional problem with a nonlocal condition. We establish a blow up result for large initial data and a decay result for small initial data.
Said Mesloub, Salim A. Messaoudi
doaj  

From Stability to Chaos: A Complete Classification of the Damped Klein‐Gordon Dynamics

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9696-9708, June 2026.
ABSTRACT We investigate the transition between stability and chaos in the damped Klein‐Gordon equation, a fundamental model for wave propagation and energy dissipation. Using semigroup methods and spectral criteria, we derive explicit thresholds that determine when the system exhibits asymptotic stability and when it displays strong chaotic dynamics ...
Carlos Lizama, Marina Murillo‐Arcila, Julio Puerta‐Fernández   +2 more
wiley   +1 more source

Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem [PDF]

, 2011
A semilinear reaction–diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter ε 2 , is considered. It can have multiple solutions.
Stynes, Martin, Kopteva, Natalia
core   +4 more sources

Convex waves grazing convex obstacles to high order [PDF]

Pure and Applied Analysis
In a recent paper [WW23] we studied the transport of oscillations in solutions to linear and some semilinear second-order hyperbolic boundary problems along rays that graze a convex obstacle to any order. We showed that high frequency exact solutions are
Jian Wang, Mark Williams
semanticscholar   +1 more source

Multiple front and pulse solutions in spatially periodic systems

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially periodic coefficients.
Lukas Bengel, Björn de Rijk
wiley   +1 more source

Long time existence of a class of contact discontinuities for second order hyperbolic balance laws

, 2009
The study of long time existence of classical smooth solutions for second order quasilinear wave equations has received much attention (see e.g. [1] and the references given there). Results were also obtained for continuous semilinear waves with gradient
P. Godin
semanticscholar   +1 more source

Recent Advances in Numerical Methods for Stochastic Differential Equations: From Classical Schemes to Wavelet‐Based Techniques

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
Stochastic processes prevail throughout fields as diverse as finance, physics, and biology, demanding increasingly sophisticated mathematical tools. These are the principal components of modeling systems influenced by random forces. The present work offers a structured examination of the solution landscape, progressing from foundational classical ...
Danamma I. Badigannavar, Harinakshi Karkera, Marko Kostic   +2 more
wiley   +1 more source

Blow‐Up Criteria for Higher Order Fractional Moore–Gibson–Thompson Equations With Fractional Laplacian Damping

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper presents the first systematic analysis of critical exponents for both third and fourth‐order fractional Moore–Gibson–Thompson (MGT) equations with combined spatiotemporal fractional derivatives and structural damping. We establish sharp nonexistence results for global solutions via an adapted test function method, deriving explicit critical ...
Ahlem Merah, Hussien Albala, Fares Yazid, Hicham Saber, Mohammed Almalahi, Abdelkader Moumen, Khaled Aldwoah, Smritijit Sen   +7 more
wiley   +1 more source

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