On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs

DOI10.1080/07362994.2020.1857268OpenAlexW3111329900MaRDI QIDQ5859962

Gaurav Dhariwal, Florian Huber, Alexandra Neamţu

Publication date: 18 November 2021

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.10318

zbMATH Keywords

weak solutioncross-diffusion systemspathwise mild solutionquasilinear SPDEs

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Weak solutions to PDEs (35D30)

Cites Work

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• Analysis of degenerate cross-diffusion population models with volume filling
• SPDE in Hilbert space with locally monotone coefficients
• Degenerate parabolic stochastic partial differential equations: quasilinear case
• Exponential attractors for competing species model with cross-diffusions
• Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
• Semigroups of linear operators and applications to partial differential equations
• Stochastic heat equation with random coefficients
• Regularity properties of the evolution operator for abstract linear parabolic equations
• Entropy solutions for nonlinear degenerate problems
• Stochastic evolution equations with random generators
• Forward, backward and symmetric stochastic integration
• On a nonlinear elliptic-parabolic problem
• Entropy solutions for stochastic porous media equations
• Quasilinear parabolic stochastic evolution equations via maximal \(L^p\)-regularity
• Quasilinear SPDEs via rough paths
• Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise
• Strong solutions for stochastic partial differential equations of gradient type
• Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
• The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations
• Global martingale solutions for quasilinear SPDEs via the boundedness-by-entropy method
• Pathwise mild solutions for quasilinear stochastic partial differential equations
• Global martingale solutions for a stochastic population cross-diffusion system
• Quasilinear generalized parabolic Anderson model equation
• Weak solutions of the Shigesada-Kawasaki-Teramoto equations and their attractors
• A concise course on stochastic partial differential equations
• Quasilinear parabolic stochastic partial differential equations: existence, uniqueness
• Paracontrolled quasilinear SPDEs
• A new approach to stochastic evolution equations with adapted drift
• Abstract Parabolic Evolution Equations and their Applications
• Quasilinear Evolution Equations and Parabolic Systems
• Initial Boundary Value Problems and Optimal Control for Nonautonomous Parabolic Systems
• Shorter Notes: Strongly Continuous Semigroups, Weak Solutions, and the Variation of Constants Formula
• Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization
• A Solution Theory for Quasilinear Singular SPDEs
• Forward integration, convergence and non-adapted pointwise multipliers
• A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type
• Stochastic quasilinear evolution equations in UMD Banach spaces
• Stochastic Equations in Infinite Dimensions

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