Stochastic NonLinear Wave Equations in Local Sobolev Spaces

By Martin Ondrej'at. 2010

69 citations recorded by the source corpus.

Existence of weak solutions of stochastic wave equations with nonlinearities of a critical growth driven by spatially homogeneous Wiener processes is established in local Sobolev spaces and local energy estimates for these solutions are proved. A new method to construct weak solutions is employed.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/688e3afbcd15f95c4fe5d41dcf0b5c81ee313362

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Martina Hofmanov'a
2. Zdzisław Brzeźniak
3. Arnaud Debussche
4. Julien Vovelle
5. Martin Ondrej'at
6. El.zbieta Motyl
7. J. V. Neerven
8. Xicheng Zhang

In Finance

1. Martina Hofmanov'a
2. Zdzisław Brzeźniak
3. Arnaud Debussche
4. Julien Vovelle
5. Martin Ondrej'at
6. El.zbieta Motyl
7. Benjamin Gess
8. Panagiotis E. Souganidis

In Mathematical Physics

1. Martina Hofmanov'a
2. Zdzisław Brzeźniak
3. Arnaud Debussche
4. Julien Vovelle
5. Martin Ondrej'at
6. El.zbieta Motyl
7. J. V. Neerven
8. Fabian Hornung

Citations in the corpus

• Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces (2011, background): “The proofs of them can be found in [47]; see Corollary B.”
• Degenerate parabolic stochastic partial differential equations (2013, background): “First applications were already done in [3,25] and, in the finite-dimensional case, also in [19].”
• Degenerate parabolic stochastic partial differential equations: Quasilinear case (2013, methodology): “For other applications of this method, we refer the reader to [3, 12, 14, 24].”