Parabolic SPDEs degenerating on the boundary of nonsmooth domain.

Kim, Kyeong-Hun

Displaying similar documents to “Parabolic SPDEs degenerating on the boundary of nonsmooth domain.”

Existence of solutions of the Cauchy problem for semilinear infinite systems of parabolic differential-functional equations.

Pudełko, Anna (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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$L_{\infty}$ -estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski (1996)

Banach Center Publications

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Existence of weak solutions and an $L_{\infty}$ -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_{\infty}$ -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.

Higher integrability for weak solutions of higher order degenerate parabolic systems.

Bögelein, Verena (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Time-dependent backward stochastic evolution equations.

Al-Hussein, AbdulRahman (2007)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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$L_{\infty}$ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

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We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_{\infty}$ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_{\infty}$ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_{\infty}$ -estimates are obtained by the Di Benedetto methods.

Study of global solutions of parabolic equations via a priori estimates III. Equations of p-Laplacian type

Gary Lieberman (1996)

Banach Center Publications

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Strong and weak solutions to stochastic inclusions

Michał Kisielewicz (1995)

Banach Center Publications

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Existence of strong and weak solutions to stochastic inclusions $x_{t} - x_{s} \in \int_{s}^{t} F_{τ} (x_{τ}) d τ + \int_{s}^{t} G_{τ} (x_{τ}) d w_{τ} + \int_{s}^{t} \int_{ℝ^{n}} H_{τ, z} (x_{τ}) q (d τ, d z)$ and $x_{t} - x_{s} \in \int_{s}^{t} F_{τ} (x_{τ}) d τ + \int_{s}^{t} G_{τ} (x_{τ}) d w_{τ} + \int_{s}^{t} \int_{| z | \leq 1} H_{τ, z} (x_{τ}) q (d τ, d z) + \int_{s}^{t} \int_{| z | > 1} H_{τ, z} (x_{τ}) p (d τ, d z)$ , where p and q are certain random measures, is considered.

Reflected diffusions defined via the extended Skorokhod map.

Ramanan, Kavita (2006)

Electronic Journal of Probability [electronic only]

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Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities II. Local and global solvability results

Arina A. Arkhipova (2001)

Commentationes Mathematicae Universitatis Carolinae

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We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution is smooth almost everywhere and has an at most finite number of singular points.

On uniqueness for a system of heat equations coupled in the boundary conditions.

Kordoš, M. (2004)

Acta Mathematica Universitatis Comenianae. New Series

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Existence of local solutions for free boundary problems for viscous compressible barotropic fluids

W. M. Zajączkowski (1995)

Annales Polonici Mathematici

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We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].

Neumann problem for one-dimensional nonlinear thermoelasticity

Yoshihiro Shibata (1992)

Banach Center Publications

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The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.