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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27549 |
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| _version_ | 1866914520218206208 |
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| author | Li, Chunjin Li, Shijun Xu, Shaopeng |
| author_facet | Li, Chunjin Li, Shijun Xu, Shaopeng |
| contents | We consider a class of nonlinear parabolic equations
\[
\dfrac{\partial}{\partial t} b(u)-\nabla \cdot (A(x,t,u,\nabla u))+H(x,t,\nabla u)=f ,
\]
where $H$ is a nonlinear lower order term satisfied the Carath$\acute{e}$odory condition and
\[
\left\lvert H(x,t,\nabla u)\right\rvert\leqslant g(x,t)\left\lvert \nabla u\right\rvert^{δ(x)}
\]
with
\[
δ(x)=\frac{p(x)(N+1)-N}{(N+2)(p(x)-1)}(p^--1) \quad \text{and} \quad p^-=\underset{x\in\barΩ}{min}\,p(x).
\]
By virtue of truncation metheod,the monotone operator theory
and a gradient estimate we prove existence of renormalized solutions without coercivity condition on lower order term in the framework of variable exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Renormalized Solutions for a Class of Nonlinear Parabolic Equation with a Lower Order Term and Variable Exponents Li, Chunjin Li, Shijun Xu, Shaopeng Analysis of PDEs We consider a class of nonlinear parabolic equations \[ \dfrac{\partial}{\partial t} b(u)-\nabla \cdot (A(x,t,u,\nabla u))+H(x,t,\nabla u)=f , \] where $H$ is a nonlinear lower order term satisfied the Carath$\acute{e}$odory condition and \[ \left\lvert H(x,t,\nabla u)\right\rvert\leqslant g(x,t)\left\lvert \nabla u\right\rvert^{δ(x)} \] with \[ δ(x)=\frac{p(x)(N+1)-N}{(N+2)(p(x)-1)}(p^--1) \quad \text{and} \quad p^-=\underset{x\in\barΩ}{min}\,p(x). \] By virtue of truncation metheod,the monotone operator theory and a gradient estimate we prove existence of renormalized solutions without coercivity condition on lower order term in the framework of variable exponents. |
| title | Renormalized Solutions for a Class of Nonlinear Parabolic Equation with a Lower Order Term and Variable Exponents |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.27549 |