Fractional nonlinear stochastic heat equation with variable thermal conductivity
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Miloš Japundžić
Abstract
We consider a nonlinear stochastic heat equation with Riesz space-fractional derivative and variable thermal conductivity, on infinite domain. First we approximate the original problem by regularizing the Riesz space-fractional derivative. Then we prove that the approximate problem has almost surely a unique solution within a Colombeau generalized stochastic process space. In our solving procedure we use the theory of Colombeau generalized uniformly continuous semigroups of operators. At the end, we study the relation of the original and the approximate problem and prove that, under certain conditions, the derivative operators appearing in these two problems are associated. Even more, we prove that under some additional conditions, solutions of the original and the approximate problem are almost certainly associated as well (assuming that the first one almost surely exists).
Editorial Note: This paper has been presented at the online international conference “FCTFA 2020: Topics in Fractional Calculus and Time-frequency Analysis”, University of Novi Sad, Serbia, 16–17 June 2020.
Acknowledgements
The paper is under the bilateral project between the Bulgarian Academy of Sciences and the Serbian Academy of Sciences and Arts through the project Operators, Differential Equations and Special Functions of Fractional Calculus - Numerics and Applications.
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© 2020 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA special 2020 conferences' issue (FCAA–Volume 23–6–2020)
- Survey Paper
- Wave propagation dynamics in a fractional Zener model with stochastic excitation
- A survey on numerical methods for spectral Space-Fractional diffusion problems
- Research Paper
- Determination of the order of fractional derivative for subdiffusion equations
- Multidimensional van der Corput-Type estimates involving Mittag-Leffler functions
- Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data
- Uniqueness for an inverse source problem of determining a space-dependent source in a non-autonomous time-fractional diffusion equation
- Nakhushev extremum principle for a class of integro-differential operators
- Bounded solutions of second order of accuracy difference schemes for semilinear fractional schrödinger equations
- Fractional nonlinear stochastic heat equation with variable thermal conductivity
- Implementation of fractional optimal control problems in real-world applications
- Historical Survey
- Mkhitar Djrbashian and his contribution to Fractional Calculus
- Archive Paper
- Fractional derivatives and cauchy problem for differential equations of fractional order
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA special 2020 conferences' issue (FCAA–Volume 23–6–2020)
- Survey Paper
- Wave propagation dynamics in a fractional Zener model with stochastic excitation
- A survey on numerical methods for spectral Space-Fractional diffusion problems
- Research Paper
- Determination of the order of fractional derivative for subdiffusion equations
- Multidimensional van der Corput-Type estimates involving Mittag-Leffler functions
- Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data
- Uniqueness for an inverse source problem of determining a space-dependent source in a non-autonomous time-fractional diffusion equation
- Nakhushev extremum principle for a class of integro-differential operators
- Bounded solutions of second order of accuracy difference schemes for semilinear fractional schrödinger equations
- Fractional nonlinear stochastic heat equation with variable thermal conductivity
- Implementation of fractional optimal control problems in real-world applications
- Historical Survey
- Mkhitar Djrbashian and his contribution to Fractional Calculus
- Archive Paper
- Fractional derivatives and cauchy problem for differential equations of fractional order
