Weak solutions and invariant measures for some class of SPDE’s

In this paper, we study the stochastic reaction–diffusion equations in the case when the reaction coefficient does not satisfy the traditional sign and growth conditions. We establish existence of a weak solution and investigate the long-time behavior in terms of the existence of invariant measure.

Authors

Oleksiy V. Kapustyan (ORCID: https://orcid.org/0000-0002-9373-6812)
Viktoriia Mogylova
Andriy Stanzhytsky
Oleksandr Stanzhytskyi (ORCID: https://orcid.org/0009-0008-7587-1608)

Institutions

Taras Shevchenko National University of Kyiv (UA)
Institute of Mathematics (UA)
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” (UA)

Publication Details

Journal: Stochastics and Dynamics
Published: 2025-03-01
DOI: https://doi.org/10.1142/s0219493725500108
Primary Topic: Stability and Controllability of Differential Equations
Type: article
Field-Weighted Citation Impact: 0.00

Controls

|||

ALL TIME

JAN

FEB

MAR

APR

MAY

JUN

JUL

AUG

SEP

OCT

article

Weak solutions and invariant measures for some class of SPDE’s

Oleksiy V. Kapustyan, Viktoriia Mogylova, Andriy Stanzhytsky, Oleksandr Stanzhytskyi

Mar 1, 2025

Stochastics and Dynamics

Stability and Controllability of Differential Equations

article

Weak solutions and invariant measures for some class of SPDE’s

Oleksiy V. Kapustyan, Viktoriia Mogylova, Andriy Stanzhytsky, Oleksandr Stanzhytskyi

March 1, 2025article en

Abstract

In this paper, we study the stochastic reaction–diffusion equations in the case when the reaction coefficient does not satisfy the traditional sign and growth conditions. We establish existence of a weak solution and investigate the long-time behavior in terms of the existence of invariant measure.

Stochastics and DynamicsVol. 25(02)

Taras Shevchenko National University of Kyiv (UA), Institute of Mathematics (UA), National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” (UA)

Openalex Percentile: Top 95%

Stability and Controllability of Differential Equations

DOI Source OpenAlex

AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Weak solutions and invariant measures for some class of SPDE’s — Oleksiy V. Kapustyan, Viktoriia Mogylova, et al. · Stochastics and Dynamics (2025) | TGRS Research Map | TGRS