Seminars&Colloquia
- Colloquium: Support properties of solutions of nonlinear stochastic reaction-diffusion equations
- saarc |
- 2024-05-08 11:19:12|
- 188
- 2024-05-08 11:19:12|
- 일시
- 2024.05.01.(Wed.) 16:00-17:00
- 장소
- Rm.1401
- 연사
- 한범석 교수
-Title: Support properties of solutions of nonlinear stochastic reaction-diffusion equations
-Abstract: In this talk, we will introduce support properties of solutions to nonlinear stochastic reaction-diffusion equations driven by random noise ˙W : ∂tu = aijuxixj + biuxi + cu + ξσ(u) ˙W , (ω, t, x) ∈ Ω × R+ × Rd; u(0, ·) = u0, where aij , bi, c and ξ are bounded and random coefficients. The noise ˙W is spacetime white noise or spatially homogeneous colored noise satisfying reinforced Dalang’s condition. We present examples of conditions on σ(u) that guarantee the compact support property of the solution. In addition, we suggest potential generalization of these conditions.
This is joint work with Kunwoo Kim and Jaeyun Yi.
-Abstract: In this talk, we will introduce support properties of solutions to nonlinear stochastic reaction-diffusion equations driven by random noise ˙W : ∂tu = aijuxixj + biuxi + cu + ξσ(u) ˙W , (ω, t, x) ∈ Ω × R+ × Rd; u(0, ·) = u0, where aij , bi, c and ξ are bounded and random coefficients. The noise ˙W is spacetime white noise or spatially homogeneous colored noise satisfying reinforced Dalang’s condition. We present examples of conditions on σ(u) that guarantee the compact support property of the solution. In addition, we suggest potential generalization of these conditions.
This is joint work with Kunwoo Kim and Jaeyun Yi.
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