![](images/spacer.gif) |
|
|
| | | | | |
|
|
|
|
|
On the Unique Solvability of Some Nonlinear Stochastic PDEs
|
Hyek Yoo, University of Minnesota |
Abstract
The Cauchy problem for 1-dimensional nonlinear stochastic partial differential
equations is studied. The uniqueness and existence of solutions in
$cH^2_p(T)$-space are proved.
|
Full text: PDF
Pages: 1-22
Published on: September 2, 1998
|
Bibliography
-
N.U. Ahmed,
An existence theorem for stochastic
nonlinear evolution equations on Banach space,
Stoch. Anal. Appl., 10(4) (1992), 379-385.
Math Review link
-
A. Bensoussan,
Some existence results for
stochastic partial differential equations,
in Stochastic
Partial Differential Equations and Applications, G. Da Prato and
L. Tubaro, eds., Pitman Res. Notes Math. Ser., 268 (1992), 37-53.
Math Review link
-
A. Bensoussan, R. Temam,
Equations aux d'eriv'ees
partielles stochastiques non lin'eaires (1),
Israel J. Math., 11, No. 1 (1972), 95-129.
Math Review link
-
A. Bensoussan, R. Temam,
Equations stochastiques du type Navier-Stokes,
J. Funct. Anal., 13, No. 2 (1973), 195-222.
Math Review link
-
Yu.L. Dalecky, N.Yu. Goncharuk,
On a quasilinear stochastic differential equation of parabolic
type,
Stoch. Anal. Appl., 12(1) (1994), 103-129.
Math Review link
-
G. Da Prato, L. Tubaro,
Fully nonlinear stochastic partial differential equations,
SIAM J. Math. Anal. Vol.27, No. 1 (1996), 40-55.
Math Review link
-
G. Da Prato, J. Zabczyk,
Stochastic equations in infinite dimensions,
Cambridge University Press, New York, NY, 1992.
-
N.V.Krylov,
On $L_p$-theory of stochastic
partial differential equations in the whole space,
SIAM J. Math. Anal. Vol.27, No.2 (1996), 313-340.
Math Review link
-
N.V. Krylov,
An analytic approach to SPDEs,
in Stochastic Partial Differential Equations, Six Perspectives,
Mathematical Surveys and Monographs, AMS, submitted.
-
N.V. Krylov,
Nonlinear elliptic and parabolic equations of the second order,
D.Reidel, Dordrect, 1987.
Math Review link
-
N.V. Krylov,
On explicit formula for solutions
of evolutionary SPDEs (a kind of introduction to the theory),
Lecture Notes in Control and Inform. Sci., Vol. 176 (1992), 153-164.
-
N.V. Krylov,
Introduction to the theory of diffusion processes,
Amer. Math. Soc., Providence, RI, 1995.
Math Review link
-
N.V. Krylov, B.L. Rozovskii,
Stochastic evolution equations,
J. Sov. Math., 16 (1981), 1233-1277.
Math Review link
-
N.V. Krylov, B.L. Rozovskii,
Stochastic
partial differential equations and diffusion processes,
Russian Math. Surveys, 37 (1982), 81-105.
Math Review link
-
O.A. Ladyzenskaya, V.V. Solonnikov, N.N. Ural'tseva,
Linear and quasilinear equations of parabolic type,
Transl AMS, Vol. 23, Am. Math. Soc. Providence, RI, 1968.
-
E. Pardoux,
Equations aux deriv'ees partielles
stochastiques nonlin'eaires monotones, Th`ese, Universit'e
Paris XI, 1975
-
E. Pardoux,
Stochastic partial differential
equations and filtering of diffusion processes,
Stochastics, Vol.3 (1979), 127-167.
Math Review link
-
B.L.Rozovskii,
Stochastic evolution systems,
Kluwer, Dordrecht, 1990.
Math Review link
-
L. Tubaro,
Some results on stochastic partial
differential equations by the stochastic characteristics method,
Stoch. Anal. Appl., 6(2) (1988), 217-230.
Math Review link
-
H. Yoo,
$L_p$-estimates for stochastic PDEs with
discontinuous coefficients,
to appear in Stoch. Anal. Appl.
|
|
|
|
|
|
|
| | | | |
Electronic Journal of Probability. ISSN: 1083-6489 |
|