Reaction-diffusion equations with transport noise and critical superlinear diffusion: global well-posedness of weakly dissipative systems

DOI10.1137/23m1562482zbMATH Open1543.35093MaRDI QIDQ6571038

Mark C. Veraar, Antonio Agresti

Publication date: 11 July 2024

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

regularityglobal well-posednessreaction-diffusion equationsLotka-Volterra equationspredator-prey systemsAllen-Cahn equationstochastic evolution equationsblow-up criteriaBrusselatorweak dissipativityweak coercivitycoagulation dynamicsstochastic maximal regularitysemilinear SPDEs

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Abstract parabolic equations (35K90) Reaction-diffusion equations (35K57) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Equations in function spaces; evolution equations (58D25) Blow-up in context of PDEs (35B44) Harmonic analysis and PDEs (42B37)

Cites Work

• Tightness for a stochastic Allen-Cahn equation
• Continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations
• Stochastic partial differential equations: an introduction
• Stochastic Allen-Cahn approximation of the mean curvature flow: large deviations upper bound
• Global existence in reaction-diffusion systems with control of mass: a survey
• Degenerate parabolic stochastic partial differential equations: quasilinear case
• Global solutions of reaction-diffusion systems
• Spatial patterns in coupled biochemical oscillators
• Long-time existence for signed solutions of the heat equation with a noise term
• Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
• A contribution to the mathematical theory of epidemics.
• The elements of physical biology.
• Global solutions to stochastic reaction-diffusion equations with super-linear drift and multiplicative noise
• Sharp interface limit for stochastically perturbed mass conserving Allen-Cahn equation
• Large deviation principle for a stochastic Allen-Cahn equation
• The critical parameter for the heat equation with a noise term to blow up in finite time.
• Global dissipative dynamics of the extended Brusselator system
• On the symbiotic Lotka-Volterra model with diffusion and transport effects
• Existence and uniqueness for the mild solution of the stochastic heat equation with non-Lipschitz drift on an unbounded spatial domain
• Long-time behavior of stochastic reaction-diffusion equation with multiplicative noise
• Random separation property for stochastic Allen-Cahn-type equations
• From additive to transport noise in 2D fluid dynamics
• Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations
• Nonlinear parabolic stochastic evolution equations in critical spaces. II: Blow-up criteria and instantaneous regularization
• \(L^p\)-estimates and regularity for SPDEs with monotone semilinearity
• On the bidomain equations driven by stochastic forces
• Analysis of three species Lotka-Volterra food web models with omnivory
• A stochastic reaction-diffusion equation with multiplicative noise
• Global classical solutions to quadratic systems with mass control in arbitrary dimensions
• On the boundedness of solutions of SPDEs
• Parabolic equations in biology. Growth, reaction, movement and diffusion
• A Khasminskii type averaging principle for stochastic reaction-diffusion equations
• Stabilization by noise for a class of stochastic reaction-diffusion equations
• Invasibility and stochastic boundedness in monotonic competition models
• Stochastic Lotka-Volterra competitive reaction-diffusion systems perturbed by space-time white noise: modeling and analysis
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• Analysis in Banach Spaces
• ON UNIQUENESS OF MILD SOLUTIONS FOR DISSIPATIVE STOCHASTIC EVOLUTION EQUATIONS
• Stable Coexistence States in the Volterra–Lotka Competition Model with Diffusion
• Dynamics of the lotka-volterra systems with diffusion
• Long time existence for the heat equation with a spatially correlated noise term
• Uniqueness and nonuniqueness of coexistence states in the lotka‐volterra competition model
• Blowup in Reaction-Diffusion Systems with Dissipation Of Mass
• On Well-Posedness of Semilinear Stochastic Evolution Equations on $L_p$ Spaces
• Global bifurcation in the Brusselator system
• Existence and uniqueness of global solutions to the stochastic heat equation with superlinear drift on an unbounded spatial domain
• Global solutions to the stochastic reaction-diffusion equation with superlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain
• Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence*
• Dynamics of Stochastic Reaction-Diffusion Equations
• Stochastic Reaction-Diffusion Systems With Hölder Continuous Multiplicative Noise
• Superlinear Parabolic Problems
• Small-Scale Structure of a Scalar Field Convected by Turbulence
• Stochastic Integration in Banach Spaces – a Survey
• Motion of a Droplet for the Stochastic Mass-Conserving Allen--Cahn Equation
• Coagulation dynamics under environmental noise: scaling limit to SPDE
• On the trace embedding and its applications to evolution equations
• Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity
• Sharp convex generalizations of stochastic Gronwall inequalities
• Stochastic maximal \(L^p( L^q)\)-regularity for second order systems with periodic boundary conditions
• The critical variational setting for stochastic evolution equations
• Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations
• Well-posedness of stochastic partial differential equations with fully local monotone coefficients
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