GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS AND DIFFUSION PROCESSES

DOI10.1142/S0219493712003523zbMath1250.35065OpenAlexW2078344231MaRDI QIDQ2888806

Wojbor A. Woyczyński, Yana I. Belopolskaya

Publication date: 4 June 2012

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493712003523

zbMATH Keywords

stochastic flowsbackward Kolmogorov equationtwo-component Markov processKunita theory

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Integral representations of solutions to PDEs (35C15) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Weak solutions to PDEs (35D30) Initial value problems for second-order parabolic systems (35K45)

Related Items (7)

Probabilistic model for the Lotka-Volterra system with cross-diffusion ⋮ Stochastic interpretation of the MHD-Burgers system ⋮ Probabilistic interpretation of the Cauchy problem solution for systems of nonlinear parabolic equations ⋮ Probabilistic models of the conservation and balance laws in switching regimes ⋮ Systems of Nonlinear Backward and Forward Kolmogorov Equations: Generalized Solutions ⋮ Probabilistic interpretations of quasilinear parabolic systems ⋮ Probabilistic Counterparts for Strongly Coupled Parabolic Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Generalized solutions of nonlinear parabolic equations and diffusion processes
• Stochastic flows acting on Schwartz distributions
• Generalized solutions of a stochastic partial differential equation
• A probabilistic approach for nonlinear equations involving the fractional Laplacian and a singular operator
• On certain systems of parabolic equations

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