Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives

Abstract

In this paper we develop a method to solve evolution equations on Gelfand triples with time-fractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasi-linear partial differential equations with time-fractional derivatives, including time-fractional (stochastic) porous media equations (including the case where the Laplace operator is also fractional) and $p$-Laplace equations as special cases.

published version in SIAM Journal on Mathematical Analysis

References in corpus (6)

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• Fractional diffusion equations and processes with randomly varying time
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Cited by in corpus (8)

• A linear Galerkin numerical method for a quasilinear subdiffusion equation
• Distribution Dependent Stochastic Porous Media Equations
• Inverse initial problem for fractional reaction-diffusion equation with nonlinearities
• Small Time Asymptotics for SPDEs with Locally Monotone Coefficients
• A Sobolev space theory for the time-fractional stochastic partial differential equations driven by Levy processes
• Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations
• Freidlin-Wentzell Type Large Deviation Principle for Multi-Scale Locally Monotone SPDEs
• On the asymptotic behavior of solutions to time-fractional elliptic equations driven a multiplicative white noise