In the present paper we deal with stochastic semilinear partial differential equations of parabolic type with (t, x)-depending coefficients which may admit a polynomial growth with respect to the space variable. Under suitable assumptions on the coefficients of the parabolic operator L associated to the equation, on the initial data and on the stochastic noise (more precisely, on the spectral measure associated with the noise) we prove existence of a unique (mild) function-valued solution for the associated Cauchy problem.
Solution Theory to Semilinear Parabolic Stochastic Partial Differential Equations with Polynomially Bounded Coefficients
ALESSIA ASCANELLI
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In corso di stampa
Abstract
In the present paper we deal with stochastic semilinear partial differential equations of parabolic type with (t, x)-depending coefficients which may admit a polynomial growth with respect to the space variable. Under suitable assumptions on the coefficients of the parabolic operator L associated to the equation, on the initial data and on the stochastic noise (more precisely, on the spectral measure associated with the noise) we prove existence of a unique (mild) function-valued solution for the associated Cauchy problem.File in questo prodotto:
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