From Brownian-Time Brownian Sheet to a Fourth Order and a Kuramoto–Sivashinsky-Variant Interacting PDEs Systems

摘要: We introduce n-parameter ℝ d -valued Brownian-time Brownian sheet (BTBS): a where each “time” parameter is replaced with the modulus of an independent motion. then connect BTBS to new system n linear, fourth order, and interacting PDEs corresponding order nonlinear PDE. The coupling phenomenon result interaction between sheet, through its variance, motions in BTBS; it leads intricate, intriguing, random field generalization our earlier Brownian-time-processes (BTPs) connection linear PDEs. Our does not belong classical theory fields; prove connections, we generalize BTP approach [4, 5] mix PDE system, which also give along second 2nth that sheet. In addition, introdu...