메뉴 건너뛰기




Volumn 27, Issue 2, 2007, Pages 183-197

On a stochastic partial differential equation with non-local diffusion

Author keywords

Fourier transform; Fractional derivative operator; Nonlocal diffusion; Space time white noise; Stochastic partial differential equation

Indexed keywords


EID: 34547288280     PISSN: 09262601     EISSN: 1572929X     Source Type: Journal    
DOI: 10.1007/s11118-007-9052-6     Document Type: Article
Times cited : (12)

References (15)
  • 1
    • 0001359254 scopus 로고
    • Modified dissipativity for a nonlinear evolution equation arising in turbulence
    • Bardos, C., Penel, P., Frisch, U., Sulem P.L.: Modified dissipativity for a nonlinear evolution equation arising in turbulence. Arch. Rational Mech. Anal. 71, 237-256 (1979)
    • (1979) Arch. Rational Mech. Anal. , vol.71 , pp. 237-256
    • Bardos, C.1    Penel, P.2    Frisch, U.3    Sulem, P.L.4
  • 2
    • 0009095592 scopus 로고
    • Stochastic integrals in the plane
    • Cairoli, R., Walsh, J.B.: Stochastic integrals in the plane. Acta Math. 134, 111-183 (1975)
    • (1975) Acta Math. , vol.134 , pp. 111-183
    • Cairoli, R.1    Walsh, J.B.2
  • 3
    • 0007210750 scopus 로고    scopus 로고
    • Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.'s
    • Dalang, R.C.: Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.'s. Electron. J. Probab. 4, 1-29 (1999)
    • (1999) Electron. J. Probab. , vol.4 , pp. 1-29
    • Dalang, R.C.1
  • 4
    • 0009253984 scopus 로고
    • Generalized solutions of a class of nuclear-space-valued stochastic evolution equations
    • Dawson, D.A., Gorostiza L.G.: Generalized solutions of a class of nuclear-space-valued stochastic evolution equations. Appl. Math. Optim. 22, 241-263 (1990)
    • (1990) Appl. Math. Optim. , vol.22 , pp. 241-263
    • Dawson, D.A.1    Gorostiza, L.G.2
  • 5
    • 0141648426 scopus 로고    scopus 로고
    • Global solution and smoothing effect for a non-local regularization of a hyperbolic equation
    • 3
    • Droniou, J., Gallouet, T., Vovelle, J.: Global solution and smoothing effect for a non-local regularization of a hyperbolic equation. J. Evol. Equ. 3(3), 499-521 (2003)
    • (2003) J. Evol. Equ. , vol.3 , pp. 499-521
    • Droniou, J.1    Gallouet, T.2    Vovelle, J.3
  • 6
    • 33747469213 scopus 로고    scopus 로고
    • Fractal first order partial differential equations
    • Droniou, J., Imbert, C.: Fractal first order partial differential equations. Arch. Rational Mech. Anal. 182, 229-261 (2004)
    • (2004) Arch. Rational Mech. Anal. , vol.182 , pp. 229-261
    • Droniou, J.1    Imbert, C.2
  • 8
    • 84972578792 scopus 로고
    • On the martingale problem for genarators of stable processes with perturbations
    • Komatsu, T.: On the martingale problem for genarators of stable processes with perturbations. Osaka J. Math. 21, 113-132 (1984)
    • (1984) Osaka J. Math. , vol.21 , pp. 113-132
    • Komatsu, T.1
  • 10
    • 0035281274 scopus 로고    scopus 로고
    • Growing fractal interfaces in the presence of self-similar hopping surface diffusion
    • Mann, J.A., Woyczynski, W.A.: Growing fractal interfaces in the presence of self-similar hopping surface diffusion. Phys. A 291, 159-183 (2001)
    • (2001) Phys. A , vol.291 , pp. 159-183
    • Mann, J.A.1    Woyczynski, W.A.2
  • 11
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler, R., Klafter J.: The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1-77 (2000)
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 12
    • 0037659276 scopus 로고
    • Stochastic partial differential equations, a review
    • Pardoux, E.: Stochastic partial differential equations, a review. Bull. Sci. Math., II Série 117, 29-47 (1979)
    • (1979) Bull. Sci. Math., II Série , vol.117 , pp. 29-47
    • Pardoux, E.1
  • 14
    • 0000775921 scopus 로고
    • Diffusion processes associated with Lévy generators
    • Stroock, D.W.: Diffusion processes associated with Lévy generators. Z. Wahrscheinlichkeitstheor. Verw. Geb. 32, 209-244 (1975)
    • (1975) Z. Wahrscheinlichkeitstheor. Verw. Geb. , vol.32 , pp. 209-244
    • Stroock, D.W.1
  • 15
    • 0000659593 scopus 로고
    • An introduction to stochastic partial differential equations. Ecole d'Eté de Probabilités de Saint-Flour XIV 1984
    • Springer Berlin, Heidelberg, New York
    • Walsh, J.B.: An introduction to stochastic partial differential equations. Ecole d'Eté de Probabilités de Saint-Flour XIV 1984. In: Lecture Notes in Mathematics, vol. 1180, pp. 265-437. Springer, Berlin, Heidelberg, New York (1986)
    • (1986) Lecture Notes in Mathematics, Vol. 1180 , pp. 265-437
    • Walsh, J.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.