Zobrazeno 1 - 10
of 187
pro vyhledávání: '"Han, Beom Seok"'
We investigate the strict positivity and the compact support property of solutions to the one-dimensional nonlinear stochastic heat equation: $$\partial_t u(t,x) = \frac{1}{2}\partial^2_x u(t,x) + \sigma(u(t,x))\dot{W}(t,x), \quad (t,x)\in \mathbf{R}
Externí odkaz:
http://arxiv.org/abs/2407.06827
This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and variable-order nonlocal operators in mixed norm $L_
Externí odkaz:
http://arxiv.org/abs/2405.11969
Autor:
Han, Beom-Seok, Yi, Jaeyun
We study the existence, uniqueness, and regularity of the solution to the stochastic reaction-diffusion equation (SRDE) with colored noise $\dot{F}$: $$ \partial_t u = a^{ij}u_{x^ix^j} + b^i u_{x^i} + cu - \bar{b} u^{1+\beta} + \xi u^{1+\gamma}\dot F
Externí odkaz:
http://arxiv.org/abs/2304.11879
Autor:
Han, Beom-Seok
We present the $L_p$-solvability for stochastic time fractional Burgers' equations driven by multiplicative space-time white noise: $$ \partial_t^\alpha u = a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + \bar b^i u u_{x^i} + \partial_t^\beta\int_0^t \sigma(u
Externí odkaz:
http://arxiv.org/abs/2301.00536
We study the compact support property for solutions of the following stochastic partial differential equations: $$\partial_t u = a^{ij}u_{x^ix^j}(t,x)+b^{i}u_{x^i}(t,x)+cu+h(t,x,u(t,x))\dot{F}(t,x),\quad (t,x)\in (0,\infty)\times{\bf{R}}^d,$$ where $
Externí odkaz:
http://arxiv.org/abs/2201.04814
Autor:
Han, Beom-Seok
We introduce the uniqueness, existence, $L_p$-regularity, and maximal H\"older regularity of the solution to semilinear stochastic partial differential equation driven by a multiplicative space-time white noise: $$ u_t = au_{xx} + bu_{x} + cu + \bar
Externí odkaz:
http://arxiv.org/abs/2111.03659
Autor:
Han, Beom-Seok
We establish the $L_p$-regularity theory for a semilinear stochastic partial differential equation with multiplicative white noise: $$ du = (a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + \bar b^{i}|u|^\lambda u_{x^i})dt + \sigma^k(u)dw_t^k,\quad (t,x)\in(0,
Externí odkaz:
http://arxiv.org/abs/2111.03302
Autor:
Han, Beom-Seok, Yi, Jaeyun
Publikováno v:
In Journal of Differential Equations 15 January 2024 379:569-599
Autor:
Choi, Jae-Hwan, Han, Beom-Seok
Existence, uniqueness, and regularity of a strong solution are obtained for stochastic PDEs with a colored noise $F$ and its super-linear diffusion coefficient: $$ du=(a^{ij}u_{x^ix^j}+b^iu_{x^i}+cu)dt+\xi|u|^{1+\lambda}dF, \quad (t,x)\in(0,\infty)\t
Externí odkaz:
http://arxiv.org/abs/2001.10687
We present a weighted $L_{q}(L_{p})$-theory ($p,q\in(1,\infty)$) with Muckenhoupt weights for the equation $$ \partial_{t}^{\alpha}u(t,x)=\Delta u(t,x) +f(t,x), \quad t>0, x\in \mathbb{R}^d. $$ Here, $\alpha\in (0,2)$ and $\partial_{t}^{\alpha}$ is t
Externí odkaz:
http://arxiv.org/abs/1911.07437