Existence and Uniqueness of Solutions to Nonlinear Diffusion with Memory
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916984285822976 |
|---|---|
| author | Chen, Yixian |
| author_facet | Chen, Yixian |
| contents | This paper studies a nonlinear diffusion equation with memory: $$u_t=\nabla\cdot \big( D(x)\cdot\int_0^t K(t-s) \nabla\cdotΦ(u(x,s))ds \big)+f(x,t)$$ Where $K$ is memory Kernel and $D(x)$ is bounded. Under monotonicity and growth conditions on $Φ$, the existence and uniqueness of weak solution is established. The analysis employs Orthogonal approximation, energy estimates, and monotone operator theory. The convolution structure is handled within variational frameworks. The result provides a basis for studying memory-type diffusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and Uniqueness of Solutions to Nonlinear Diffusion with Memory Chen, Yixian Analysis of PDEs [2020] 35K55 35B45 35D30 35R60 This paper studies a nonlinear diffusion equation with memory: $$u_t=\nabla\cdot \big( D(x)\cdot\int_0^t K(t-s) \nabla\cdotΦ(u(x,s))ds \big)+f(x,t)$$ Where $K$ is memory Kernel and $D(x)$ is bounded. Under monotonicity and growth conditions on $Φ$, the existence and uniqueness of weak solution is established. The analysis employs Orthogonal approximation, energy estimates, and monotone operator theory. The convolution structure is handled within variational frameworks. The result provides a basis for studying memory-type diffusion. |
| title | Existence and Uniqueness of Solutions to Nonlinear Diffusion with Memory |
| topic | Analysis of PDEs [2020] 35K55 35B45 35D30 35R60 |
| url | https://arxiv.org/abs/2507.16659 |