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Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms. (English) Zbl 0757.35034
This paper deals with Hamilton-Jacobi equations of the form $$(SP) \quad u+\langle Ax,Du\rangle+F(x,u,Du)=0, \qquad (CP) \quad u\sb t+\langle Ax,Du\rangle+F(t,x,u,Du)=0,$$ where $A$ is an $m$-accretive operator on a Banach space $X$, $A: D(A)\to 2\sp X$ and $F:\overline{D(A)}\times R\times X\sp x\to R$ (respectively $F:\{0,T\}\times\overline{D(A)}\times R\times X\sp x\to R$) are continuous mappings. The author presents a new definition of viscosity solution for the Hamilton-Jacobi equations $(SP)$ and $(CP)$ and proves existence and uniqueness results under usual assumptions on the bounded part of the Hamiltonian.

35K55Nonlinear parabolic equations
49L25Viscosity solutions (infinite-dimensional problems)
70H20Hamilton-Jacobi equations (mechanics of particles and systems)
Full Text: DOI
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